A027002 a(n) = T(2*n, n+3), T given by A026998.

1, 43, 431, 2482, 10636, 38138, 122069, 362853, 1027843, 2822668, 7601784, 20228876, 53447609, 140633575, 369179479, 967898846, 2535852052, 6641420806, 17390705661, 45533644161, 119213967867, 312112955384, 817130734512, 2139286435768, 5600737350897

Offset

3,2

Links

Robert Israel, Table of n, a(n) for n = 3..2370

Index entries for linear recurrences with constant coefficients, signature (9,-34,71,-90,71,-34,9,-1).

Formula

G.f.: x^3*(1+34*x+78*x^2-6*x^3-11*x^4) / ((1-x)^6*(1-3*x+x^2)). - Colin Barker, Feb 18 2016

From Robert Israel, Feb 18 2016: (Start)

By definition, a(n) is the coefficient of x^(2*n-6) in the Maclaurin series of (1+2*x)/((1-x-x^2)*(1-x)^6). This can be written explicitly:

a(n) = ((29-13*sqrt(5))/2)*((3-sqrt(5))/2)^n + ((29+13*sqrt(5))/2)*((3+sqrt(5))/2)^n - (4/5)*n^5 + (4/3)*n^4 - (25/3)*n^3 - (31/3)*n^2 - (433/15)*n - 29.

This confirms Colin Barker's g.f. (End)

Maple

gf:= x^3*(1+34*x+78*x^2-6*x^3-11*x^4) / ((1-x)^6*(1-3*x+x^2)):
S:= series(gf, x, 100):
seq(coeff(S, x, n), n=3..100); # Robert Israel, Feb 18 2016

Mathematica

LinearRecurrence[{9, -34, 71, -90, 71, -34, 9, -1}, {1, 43, 431, 2482, 10636, 38138, 122069, 362853}, 30] (* Vincenzo Librandi, Feb 19 2016 *)

Prog

(PARI) Vec(x^3*(1+34*x+78*x^2-6*x^3-11*x^4)/((1-x)^6*(1-3*x+x^2)) + O(x^40)) \\ Colin Barker, Feb 19 2016

Crossrefs

Sequence in context: A142841 A142913 A228908 * A093673 A244769 A239268

Adjacent sequences: A026999 A027000 A027001 * A027003 A027004 A027005

Keyword

nonn

Author

Clark Kimberling

Status

approved