A047382 -id:A047382

Search: a047382 -id:a047382

Displaying 1-4 of 4 results found.

page 1

A047328

Numbers that are congruent to {0, 3, 5, 6} mod 7.

+10
5

0, 3, 5, 6, 7, 10, 12, 13, 14, 17, 19, 20, 21, 24, 26, 27, 28, 31, 33, 34, 35, 38, 40, 41, 42, 45, 47, 48, 49, 52, 54, 55, 56, 59, 61, 62, 63, 66, 68, 69, 70, 73, 75, 76, 77, 80, 82, 83, 84, 87, 89, 90, 91, 94, 96, 97, 98, 101, 103, 104, 105, 108, 110, 111

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,2

COMMENTS

Indices of the odd numbers in the Padovan sequence (A000931). - Francesco Daddi, Jul 31 2011

LINKS

Bruno Berselli, Table of n, a(n) for n = 1..1000

Index entries for linear recurrences with constant coefficients, signature (1,0,0,1,-1).

FORMULA

G.f.: x^2*(3+2x+x^2+x^3)/((1-x)^2*(1+x)*(1+x^2)). a(n) = A028762(n-2), 2<n<28. - R. J. Mathar, Oct 18 2008

a(n) = (1/8)*(14*n-5-(2-(-1)^n)*(1+2*(-1)^floor(n/2))). - Bruno Berselli, Aug 01 2011

From Wesley Ivan Hurt, May 31 2016: (Start)

a(n) = a(n-1) + a(n-4) - a(n-5) for n>5.

a(n) = (14*n-7+i^(2*n)-(1+3*i)*i^(-n)-(1-3*i)*i^n)/8 where i=sqrt(-1).

a(2k) = A047280(k), a(2k-1) = A047382(k). (End)

E.g.f.: (4 - 3*sin(x) - cos(x) + (7*x - 4)*sinh(x) + (7*x - 3)*cosh(x))/4. - Ilya Gutkovskiy, May 31 2016

MAPLE

A047328:=n->(14*n-7+I^(2*n)-(1+3*I)*I^(-n)-(1-3*I)*I^n)/8: seq(A047328(n), n=1..100); # Wesley Ivan Hurt, May 31 2016

MATHEMATICA

Table[(14n-7+I^(2n)-(1+3*I)*I^(-n)-(1-3*I)*I^n)/8, {n, 80}] (* Wesley Ivan Hurt, May 31 2016 *)

PROG

(PARI) a(n)=n\4*7+[0, 3, 5, 6][n%4+1] \\ Charles R Greathouse IV, Jul 31 2011

(Magma) [ n: n in [0..111] | n mod 7 in [0, 3, 5, 6] ]; // Bruno Berselli, Aug 01 2011

CROSSREFS

Cf. A000931, A047280, A047382, A134719.

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane

STATUS

approved

A047322

Numbers that are congruent to {0, 1, 5, 6} mod 7.

+10
2

0, 1, 5, 6, 7, 8, 12, 13, 14, 15, 19, 20, 21, 22, 26, 27, 28, 29, 33, 34, 35, 36, 40, 41, 42, 43, 47, 48, 49, 50, 54, 55, 56, 57, 61, 62, 63, 64, 68, 69, 70, 71, 75, 76, 77, 78, 82, 83, 84, 85, 89, 90, 91, 92, 96, 97, 98, 99, 103, 104, 105, 106, 110, 111

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,3

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Index entries for linear recurrences with constant coefficients, signature (1,0,0,1,-1).

FORMULA

a(n+1) = Sum_{k>=0} A030308(n,k)*b(k) with b(0)=1, b(1)=5, b(k)=7*2^(k-2) for k>1. - Philippe Deléham, Oct 19 2011

G.f.: x^2*(1+4*x+x^2+x^3) / ( (1+x)*(x^2+1)*(x-1)^2 ). - R. J. Mathar, Dec 03 2011

From Wesley Ivan Hurt, May 23 2016: (Start)

a(n) = a(n-1) + a(n-4) - a(n-5) for n>5.

a(n) = (14n-11-3*I^(2n)+(3-3*I)*I^(-n)+(3+3*I)*I^n)/8 where I=sqrt(-1).

a(2n) = A047336(n), a(2n-1) = A047382(n). (End)

E.g.f.: (4 - 3*sin(x) + 3*cos(x) + (7*x - 4)*sinh(x) + 7*(x - 1)*cosh(x))/4. - Ilya Gutkovskiy, May 24 2016

MAPLE

A047322:=n->(14*n-11-3*I^(2*n)+(3-3*I)*I^(-n)+(3+3*I)*I^n)/8: seq(A047322(n), n=1..100); # Wesley Ivan Hurt, May 23 2016

MATHEMATICA

Table[(14n-11-3*I^(2n)+(3-3*I)*I^(-n)+(3+3*I)*I^n)/8, {n, 80}] (* Wesley Ivan Hurt, May 23 2016 *)

LinearRecurrence[{1, 0, 0, 1, -1}, {0, 1, 5, 6, 7}, 60] (* Vincenzo Librandi, May 24 2016 *)

PROG

(Magma) [n : n in [0..150] | n mod 7 in [0, 1, 5, 6]]; // Wesley Ivan Hurt, May 23 2016

CROSSREFS

Cf. A030308, A047336, A047382.

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane

EXTENSIONS

More terms from Wesley Ivan Hurt, May 23 2016

STATUS

approved

A047312

Numbers that are congruent to {0, 4, 5, 6} mod 7.

+10
1

0, 4, 5, 6, 7, 11, 12, 13, 14, 18, 19, 20, 21, 25, 26, 27, 28, 32, 33, 34, 35, 39, 40, 41, 42, 46, 47, 48, 49, 53, 54, 55, 56, 60, 61, 62, 63, 67, 68, 69, 70, 74, 75, 76, 77, 81, 82, 83, 84, 88, 89, 90, 91, 95, 96, 97, 98, 102, 103, 104, 105, 109, 110, 111

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,2

LINKS

Daniel Starodubtsev, Table of n, a(n) for n = 1..10000

Index entries for linear recurrences with constant coefficients, signature (1,0,0,1,-1).

FORMULA

G.f.: x^2*(4+x+x^2+x^3) / ( (1+x)*(1+x^2)*(x-1)^2 ). - R. J. Mathar, Oct 25 2011

From Wesley Ivan Hurt, Jun 03 2016: (Start)

a(n) = a(n-1) + a(n-4) - a(n-5) for n>5.

a(n) = (14*n-5+3*i^(2*n)-(3+3*i)*i^(-n)-(3-3*i)*i^n)/8 where i=sqrt(-1).

a(2k) = A047288(k), a(2k-1) = A047382(k). (End)

MAPLE

A047312:=n->(14*n-5+3*I^(2*n)-(3+3*I)*I^(-n)-(3-3*I)*I^n)/8: seq(A047312(n), n=1..100); # Wesley Ivan Hurt, Jun 03 2016

MATHEMATICA

Table[(14n-5+3*I^(2n)-(3+3*I)*I^(-n)-(3-3*I)*I^n)/8, {n, 80}] (* Wesley Ivan Hurt, Jun 03 2016 *)

PROG

(Magma) [n : n in [0..150] | n mod 7 in [0, 4, 5, 6]]; // Wesley Ivan Hurt, Jun 03 2016

CROSSREFS

Cf. A047288, A047382.

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane

STATUS

approved

A047324

Numbers that are congruent to {0, 2, 5, 6} mod 7.

+10
1

0, 2, 5, 6, 7, 9, 12, 13, 14, 16, 19, 20, 21, 23, 26, 27, 28, 30, 33, 34, 35, 37, 40, 41, 42, 44, 47, 48, 49, 51, 54, 55, 56, 58, 61, 62, 63, 65, 68, 69, 70, 72, 75, 76, 77, 79, 82, 83, 84, 86, 89, 90, 91, 93, 96, 97, 98, 100, 103, 104, 105, 107, 110, 111

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,2

LINKS

Table of n, a(n) for n=1..64.

Index entries for linear recurrences with constant coefficients, signature (1,0,0,1,-1).

FORMULA

G.f.: x^2*(2+3*x+x^2+x^3) / ( (1+x)*(1+x^2)*(x-1)^2 ). - R. J. Mathar, Dec 04 2011

From Wesley Ivan Hurt, Jun 03 2016: (Start)

a(n) = a(n-1) + a(n-4) - a(n-5) for n > 5.

a(n) = (14*n - 9 - i^(2*n) + (1 - 3*i)*i^(-n) + (1 + 3*i)*i^n)/8 where i = sqrt(-1).

a(2k) = A047276(k), a(2k-1) = A047382(k). (End)

E.g.f.: (4 - 3*sin(x) + cos(x) + (7*x - 4)*sinh(x) + (7*x - 5)*cosh(x))/4. - Ilya Gutkovskiy, Jun 04 2016

MAPLE

A047324:=n->(14*n-9-I^(2*n)+(1-3*I)*I^(-n)+(1+3*I)*I^n)/8: seq(A047324(n), n=1..100); # Wesley Ivan Hurt, Jun 03 2016

MATHEMATICA

Table[(14n - 9 - I^(2n) + (1 - 3 * I) * I^(-n) + (1 + 3 * I) * I^n)/8, {n, 80}] (* Wesley Ivan Hurt, Jun 03 2016 *)

Flatten[Table[7n + {0, 2, 5, 6}, {n, 0, 15}]] (* Alonso del Arte, Jun 04 2016 *)

LinearRecurrence[{1, 0, 0, 1, -1}, {0, 2, 5, 6, 7}, 80] (* Harvey P. Dale, Jan 10 2023 *)

PROG

(Magma) [n : n in [0..150] | n mod 7 in [0, 2, 5, 6]]; // Wesley Ivan Hurt, Jun 03 2016

CROSSREFS

Cf. A047276, A047382.

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane

STATUS

approved

page 1

Search completed in 0.010 seconds