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Search: a155594 -id:a155594
Displaying 1-10 of 17 results found.
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A155599
a(n) = 8^n - 2^n + 1^n.
+10
33
1, 7, 61, 505, 4081, 32737, 262081, 2097025, 16776961, 134217217, 1073740801, 8589932545, 68719472641, 549755805697, 4398046494721, 35184372056065, 281474976645121, 2251799813554177, 18014398509219841, 144115188075331585
(list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
LINKS
Table of n, a(n) for n=0..19.
Index entries for linear recurrences with constant coefficients, signature (11,-26,16).
FORMULA
G.f.: 1/(1-8*x) - 1/(1-2*x) + 1/(1-x).
E.g.f.: e^(8*x) - e^(2*x) + e^x.
a(n) = 10*a(n-1) - 16*a(n-2) + 7 with a(0)=1, a(1)=7 - Vincenzo Librandi, Jul 21 2010
a(n) = A248217(n)+1. - R. J. Mathar, Mar 10 2022
MATHEMATICA
Table[8^n-2^n+1, {n, 0, 30}] (* or *) LinearRecurrence[{11, -26, 16}, {1, 7, 61}, 30] (* Harvey P. Dale, Feb 25 2014 *)
PROG
(PARI) a(n)=8^n-2^n+1 \\ Charles R Greathouse IV, Sep 24 2015
CROSSREFS
Cf. A074501, A020515, A155588, A155590, A155592, A155593, A155594, A155596, A155597, A155598.
KEYWORD
nonn,easy
AUTHOR
Mohammad K. Azarian, Jan 25 2009
STATUS
approved
A155596
a(n) = 5^n - 2^n + 1^n.
+10
30
1, 4, 22, 118, 610, 3094, 15562, 77998, 390370, 1952614, 9764602, 48826078, 244136530, 1220694934, 6103499242, 30517545358, 152587825090, 762939322054, 3814697003482, 19073485803838, 95367430592050, 476837156105974
(list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
LINKS
Table of n, a(n) for n=0..21.
Index entries for linear recurrences with constant coefficients, signature (8,-17,10).
FORMULA
G.f.: 1/(1-5*x)-1/(1-2*x)+1/(1-x).
E.g.f.: e^(5*x) - e^(2*x) + e^x.
a(n) = 7*a(n-1)-10*a(n-2)+4 with a(0)=1, a(1)=4. - Vincenzo Librandi, Jul 21 2010
a(n) = A005057(n)+1. - R. J. Mathar, Mar 10 2022
MATHEMATICA
Table[5^n-2^n+1, {n, 0, 30}] (* or *) LinearRecurrence[{8, -17, 10}, {1, 4, 22}, 30] (* Harvey P. Dale, Sep 11 2019 *)
PROG
(PARI) a(n)=5^n-2^n+1 \\ Charles R Greathouse IV, Sep 24 2015
CROSSREFS
Cf. A074501, A020515, A155588, A155590, A155592, A155593, A155594.
KEYWORD
nonn,easy
AUTHOR
Mohammad K. Azarian, Jan 25 2009
STATUS
approved
A155597
a(n) = 6^n - 2^n + 1.
+10
27
1, 5, 33, 209, 1281, 7745, 46593, 279809, 1679361, 10077185, 60465153, 362795009, 2176778241, 13060685825, 78364147713, 470184951809, 2821109841921, 16926659313665, 101559956406273, 609359739486209, 3656158439014401, 21936950638280705, 131621703838072833
(list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
LINKS
Table of n, a(n) for n=0..22.
Index entries for linear recurrences with constant coefficients, signature (9,-20,12).
FORMULA
G.f.: 1/(1-6*x)-1/(1-2*x)+1/(1-x).
E.g.f.: exp(6*x)-exp(2*x)+exp(x).
a(n) = 8*a(n-1)-12*a(n-2)+5 with a(0)=1, a(1)=5. - Vincenzo Librandi, Jul 21 2010
a(0)=1, a(1)=5, a(2)=33, a(n) = 9*a(n-1)-20*a(n-2)+12*a(n-3). - Harvey P. Dale, Jul 13 2011
a(n) = A248216(n)+1. - R. J. Mathar, Mar 10 2022
MATHEMATICA
Table[6^n-2^n+1, {n, 0, 20}] (* or *) LinearRecurrence[{9, -20, 12}, {1, 5, 33}, 20] (* Harvey P. Dale, Jul 13 2011 *)
PROG
(PARI) a(n) = 6^n-2^n+1 \\ Charles R Greathouse IV, Jul 25 2011
CROSSREFS
Cf. A074501, A020515, A155588, A155590, A155592, A155593, A155594, A155596.
KEYWORD
nonn,easy
AUTHOR
Mohammad K. Azarian, Jan 25 2009
STATUS
approved
A155600
a(n) = 9^n-2^n+1^n.
+10
27
1, 8, 78, 722, 6546, 59018, 531378, 4782842, 43046466, 387419978, 3486783378, 31381057562, 282429532386, 2541865820138, 22876792438578, 205891132061882, 1853020188786306, 16677181699535498, 150094635296736978
(list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
LINKS
Paolo Xausa, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (12,-29,18).
FORMULA
G.f.: 1/(1-9*x)-1/(1-2*x)+1/(1-x). E.g.f.: e^(9*x)-e^(2*x)+e^x.
a(n) = 11*a(n-1)-18*a(n-2)+8 with a(0)=1, a(1)=8 - Vincenzo Librandi, Jul 21 2010
a(n) = A191465(n)+1. - R. J. Mathar, Mar 10 2022
MATHEMATICA
Table[9^n - 2^n + 1, {n, 0, 25}] (* or *)
LinearRecurrence[{12, -29, 18}, {1, 8, 78}, 26] (* Paolo Xausa, Jul 19 2024 *)
PROG
(PARI) a(n)=9^n-2^n+1 \\ Charles R Greathouse IV, Sep 24 2015
CROSSREFS
Cf. A074501, A020515, A155588, A155590, A155592, A155593, A155594, A155596, A155597, A155598, A155599.
KEYWORD
nonn,easy
AUTHOR
Mohammad K. Azarian, Jan 25 2009
STATUS
approved
A155598
a(n) = 7^n-2^n+1.
+10
26
1, 6, 46, 336, 2386, 16776, 117586, 823416, 5764546, 40353096, 282474226, 1977324696, 13841283106, 96889002216, 678223056466, 4747561477176, 33232930504066, 232630513856136, 1628413597648306, 11398895184848856
(list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
LINKS
Table of n, a(n) for n=0..19.
Index entries for linear recurrences with constant coefficients, signature (10,-23,14).
FORMULA
G.f.: 1/(1-7*x)-1/(1-2*x)+1/(1-x). E.g.f.: e^(7*x)-e^(2*x)+e^x.
a(n) = 9*a(n-1)-14*a(n-2)+6 with a(0)=1, a(1)=6 - Vincenzo Librandi, Jul 21 2010
a(0)=1, a(1)=6, a(2)=46, a(n) = 10*a(n-1)-23*a(n-2)+14*a(n-3). - Harvey P. Dale, Feb 28 2013
a(n) = A190540(n)+1. - R. J. Mathar, Mar 10 2022
MATHEMATICA
Table[7^n-2^n+1, {n, 0, 20}] (* or *) LinearRecurrence[{10, -23, 14}, {1, 6, 46}, 20] (* Harvey P. Dale, Feb 28 2013 *)
PROG
(PARI) a(n)=7^n-2^n+1 \\ Charles R Greathouse IV, Sep 24 2015
CROSSREFS
Cf. A074501, A020515, A155588, A155590, A155592, A155593, A155594, A155596, A155597.
KEYWORD
nonn,easy
AUTHOR
Mohammad K. Azarian, Jan 25 2009
STATUS
approved
A155601
a(n) = 10^n - 2^n + 1^n.
+10
26
1, 9, 97, 993, 9985, 99969, 999937, 9999873, 99999745, 999999489, 9999998977, 99999997953, 999999995905, 9999999991809, 99999999983617, 999999999967233, 9999999999934465, 99999999999868929, 999999999999737857, 9999999999999475713, 99999999999998951425
(list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
LINKS
Table of n, a(n) for n=0..20.
Index entries for linear recurrences with constant coefficients, signature (13,-32,20).
FORMULA
G.f.: 1/(1-10*x)-1/(1-2*x)+1/(1-x).
E.g.f.: e^(10*x)-e^(2*x)+e^x.
a(n) = 12*a(n-1)-20*a(n-2)+9 with a(0)=1, a(1)=9. - Vincenzo Librandi, Jul 21 2010
a(n) = A060458(n)+1. - R. J. Mathar, Mar 10 2022
MATHEMATICA
Table[10^n-2^n+1, {n, 0, 20}] (* or *) LinearRecurrence[{13, -32, 20}, {1, 9, 97}, 20] (* Harvey P. Dale, Jan 13 2022 *)
PROG
(PARI) a(n)=10^n-2^n+1 \\ Charles R Greathouse IV, Sep 24 2015
CROSSREFS
Cf. A074501, A020515, A155588, A155590, A155592, A155593, A155594, A155596, A155597, A155598, A155599, A155600.
KEYWORD
nonn,easy
AUTHOR
Mohammad K. Azarian, Jan 25 2009
STATUS
approved
A155624
11^n-3^n+1.
+10
16
1, 9, 113, 1305, 14561, 160809, 1770833, 19484985, 214352321, 2357928009, 25937365553, 285311493465, 3138427845281, 34522710549609, 379749828800273, 4177248155066745, 45949729820525441, 505447028370153609
(list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
LINKS
Table of n, a(n) for n=0..17.
Index entries for linear recurrences with constant coefficients, signature (15,-47,33).
FORMULA
G.f.: 1/(1-11*x)-1/(1-3*x)+1/(1-x). E.g.f.: e^(11*x)-e^(3*x)+e^x.
a(n)=14*a(n-1)-33*a(n-2)+20 with a(0)=1, a(1)=9 - Vincenzo Librandi, Jul 21 2010
MATHEMATICA
LinearRecurrence[{15, -47, 33}, {1, 9, 113}, 20] (* Harvey P. Dale, Nov 02 2021 *)
PROG
(PARI) a(n)=11^n-3^n+1 \\ Charles R Greathouse IV, Jun 11 2015
CROSSREFS
Cf. A155588, A155589, A155590, A155592, A155593, A155594, A155595, A155596, A155597, A155598, A155599, A155600, A155601, A155622, A155623.
KEYWORD
nonn,easy
AUTHOR
Mohammad K. Azarian, Jan 29 2009
STATUS
approved
A155625
a(n) = 11^n + 4^n - 1.
+10
16
1, 14, 136, 1394, 14896, 162074, 1775656, 19503554, 214424416, 2358209834, 25938473176, 285315864914, 3138445153936, 34522779252794, 379750102018696, 4177249243157474, 45949734158539456, 505447045679162954, 5559917382211708216, 61159090723292453234, 672749996032071636976
(list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
LINKS
Paolo Xausa, Table of n, a(n) for n = 0..950
Index entries for linear recurrences with constant coefficients, signature (16,-59,44).
FORMULA
G.f.: 1/(1-11*x)+1/(1-4*x)-1/(1-x).
E.g.f.: exp(11*x)+exp(4*x)-exp(x).
a(n) = 15*a(n-1)-44*a(n-2)-30 with a(0) = 1, a(1) = 14. - Vincenzo Librandi, Jul 21 2010
MATHEMATICA
Table[11^n + 4^n - 1, {n, 0, 25}] (* Paolo Xausa, Jul 30 2024 *)
PROG
(PARI) a(n)=11^n+4^n-1 \\ Charles R Greathouse IV, Jun 11 2015
CROSSREFS
Cf. A155588, A155589, A155590, A155592, A155593, A155594, A155595, A155596, A155597, A155598, A155599, A155600, A155601, A155622, A155623, A155624.
KEYWORD
nonn,easy
AUTHOR
Mohammad K. Azarian, Jan 29 2009
STATUS
approved
A155626
a(n) = 5^n-4^n+1.
+10
15
1, 2, 10, 62, 370, 2102, 11530, 61742, 325090, 1690982, 8717050, 44633822, 227363410, 1153594262, 5835080170, 29443836302, 148292923330, 745759583942, 3745977788890, 18798608421182, 94267920012850, 472439111692022
(list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
LINKS
Table of n, a(n) for n=0..21.
Index entries for linear recurrences with constant coefficients, signature (10,-29,20).
FORMULA
G.f.: 1/(1-5*x)-1/(1-4*x)+1/(1-x).
E.g.f.: e^(5*x)-e^(4*x)+e^x.
a(n) = 9*a(n-1)-20*a(n-2)+12 with a(0)=1, a(1)=2. - Vincenzo Librandi, Jul 21 2010
a(n) = 10*a(n-1)-29*a(n-2)+20*a(n-3). - Wesley Ivan Hurt, Jun 07 2021
MATHEMATICA
Table[5^n-4^n+1, {n, 0, 40}] (* Vladimir Joseph Stephan Orlovsky, Feb 15 2011*)
LinearRecurrence[{10, -29, 20}, {1, 2, 10}, 30] (* Harvey P. Dale, Oct 11 2023 *)
PROG
(PARI) a(n)=5^n-4^n+1 \\ Charles R Greathouse IV, Jun 11 2015
CROSSREFS
Cf. A054401, which is essentially a(n) - 2. Also A155588, A155589, A155590, A155592, A155593, A155594, A155595, A155596, A155597, A155598, A155599, A155600, A155601, A155622, A155623, A155624, A155625.
KEYWORD
nonn,easy
AUTHOR
Mohammad K. Azarian, Jan 29 2009
STATUS
approved
A155602
4^n + 3^n - 1.
+10
13
1, 6, 24, 90, 336, 1266, 4824, 18570, 72096, 281826, 1107624, 4371450, 17308656, 68703186, 273218424, 1088090730, 4338014016, 17309009346, 69106897224, 276040168410, 1102998412176, 4408506864306, 17623567104024, 70462887356490
(list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..200
Index entries for linear recurrences with constant coefficients, signature (8,-19,12).
FORMULA
G.f.: 1/(1-4*x)+1/(1-3*x)-1/(1-x). E.g.f.: e^(4*x)+e^(3*x)-e^x.
a(n) = 7*a(n-1) - 12*a(n-2) -6, n>1 - Gary Detlefs, Jun 21 2010
a(n) = 8*a(n-1) - 19*a(n-2) + 12*a(n-3), n>2, a(0)=1, a(1)=6, a(2)=24. - L. Edson Jeffery, Oct 17 2012
a(n) = A074605(n)-1. - R. J. Mathar, Mar 10 2022
MATHEMATICA
Table[4^n + 3^n - 1, {n, 0, 50}] (* Vincenzo Librandi, Oct 17 2012 *)
LinearRecurrence[{8, -19, 12}, {1, 6, 24}, 30] (* Harvey P. Dale, Apr 28 2018 *)
PROG
(Magma) [(4^n + 3^n - 1): n in [0..30]]; // Vincenzo Librandi, Oct 17 2012
(PARI) a(n)=4^n+3^n-1 \\ Charles R Greathouse IV, Sep 24 2015
CROSSREFS
Cf. A074501, A020515, A155588, A155590, A155592-A155594, A155596-A155601.
KEYWORD
nonn,easy
AUTHOR
Mohammad K. Azarian, Jan 25 2009
STATUS
approved
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