OFFSET
6,2
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 6..5000
Index entries for linear recurrences with constant coefficients, signature (7,-21,35,-35,21,-7,1).
FORMULA
From Chai Wah Wu, Dec 29 2016: (Start)
a(n) = 7*a(n-1) - 21*a(n-2) + 35*a(n-3) - 35*a(n-4) + 21*a(n-5) - 7*a(n-6) + a(n-7) for n > 13.
G.f.: x^6*(1 + 88*x - 308*x^2 + 456*x^3 - 370*x^4 + 174*x^5 - 45*x^6 + 5*x^7)/(1-x)^7. (End)
From G. C. Greubel, Jan 22 2020: (Start)
a(n) = (n^6 + 15*n^5 - 65*n^4 - 795*n^3 + 1864*n^2 + 6180*n -7200)/720, for n > 6, with a(6) = 1.
E.g.f.: (7200 - 2880*x^2 - 960*x^3 + 30*x^4 + 60*x^5 - 5*x^6 + (-7200 + 7200*x - 720*x^2 - 720*x^3 + 150*x^4 + 30*x^5 + x^6)*exp(x))/720. (End)
MAPLE
seq( `if`(n=6, 1, (n^6 +15*n^5 -65*n^4 -795*n^3 +1864*n^2 +6180*n -7200)/720), n=6..50); # G. C. Greubel, Jan 22 2020
MATHEMATICA
Join[{1, 95, 336, 848, 1800, 3422}, LinearRecurrence[{7, -21, 35, -35, 21, -7, 1}, {6017, 9974, 15782, 24045, 35498, 51024, 71672}, 50]] (* Vincenzo Librandi, Dec 30 2016 *)
Table[If[n==6, 1, (n^6 +15*n^5 -65*n^4 -795*n^3 +1864*n^2 +6180*n -7200)/720], {n, 6, 50}] (* G. C. Greubel, Jan 22 2020 *)
PROG
(Magma) I:=[1, 95, 336, 848, 1800, 3422, 6017, 9974, 15782, 24045, 35498, 51024, 71672]; [n le 13 select I[n] else 7*Self(n-1)- 21*Self(n-2)+35*Self(n-3)-35*Self(n-4)+21*Self(n-5)-7*Self(n-6)+Self(n-7): n in [1..50]]; // Vincenzo Librandi, Dec 30 2016
(PARI) vector(45, n, my(m=n+5); if(m==6, 1, (m^6 +15*m^5 -65*m^4 -795*m^3 +1864*m^2 +6180*m -7200)/720)) \\ G. C. Greubel, Jan 22 2020
(Sage) [1]+[(n^6 +15*n^5 -65*n^4 -795*n^3 +1864*n^2 +6180*n -7200)/720 for n in (7..50)] # G. C. Greubel, Jan 22 2020
(GAP) Concatenation([1], List([7..50], n-> (n^6 +15*n^5 -65*n^4 -795*n^3 +1864*n^2 +6180*n -7200)/720 )); # G. C. Greubel, Jan 22 2020
CROSSREFS
KEYWORD
nonn
AUTHOR
Clark Kimberling, May 28 2000
STATUS
approved