A263615 Partial sums of A263614 starting at n=2.

2, 4, 8, 12, 20, 28, 44, 59, 89, 115, 167, 209, 293, 357, 485, 578, 764, 894, 1154, 1330, 1682, 1914, 2378, 2677, 3275, 3653, 4409, 4879, 5819, 6395, 7547, 8244, 9638, 10472, 12140, 13128, 15104, 16264, 18584, 19935, 22637, 24199, 27323, 29117, 32705, 34753, 38849, 41174, 45824, 48450

Offset: 2

Author

N. J. A. Sloane, Oct 23 2015

Keywords

• nonn
• base
• easy

Links

• Colin Barker, Table of n, a(n) for n = 2..1000
• G. J. Simmons, Palindromic powers, J. Rec. Math., 3 (No. 2, 1970), 93-98. [Annotated scanned copy]
• Index entries for linear recurrences with constant coefficients, signature (1,4,-4,-6,6,4,-4,-1,1).

Crossrefs

Cf. A263614.

Programs

Mathematica

LinearRecurrence[{1,4,-4,-6,6,4,-4,-1,1},{2,4,8,12,20,28,44,59,89},50] (* Harvey P. Dale, Feb 07 2024 *)

PARI

a(n) = (2*n*(3*n^3-14*n^2+147*n+272)+(4*n^3-30*n^2+128*n-27)*(-1)^n-741)/768 \\ Colin Barker, Oct 26 2015

PARI

Vec(x^2*(x^7-4*x^5-4*x^4+4*x^3+4*x^2-2*x-2)/((x-1)^5*(x+1)^4) + O(x^100)) \\ Colin Barker, Oct 26 2015

Formula

From Colin Barker, Oct 26 2015: (Start)

a(n) = (2*n*(3*n^3-14*n^2+147*n+272)+(4*n^3-30*n^2+128*n-27)*(-1)^n-741)/768.

G.f.: x^2*(x^7-4*x^5-4*x^4+4*x^3+4*x^2-2*x-2) / ((x-1)^5*(x+1)^4).

(End)