A113770 Partial sums of A113311(n)^2.

1, 10, 26, 42, 58, 74, 90, 106, 122, 138, 154, 170, 186, 202, 218, 234, 250, 266, 282, 298, 314, 330, 346, 362, 378, 394, 410, 426, 442, 458, 474, 490, 506, 522, 538, 554, 570, 586, 602, 618, 634, 650, 666, 682, 698, 714, 730, 746, 762, 778, 794

Offset

0,2

Comments

Central coefficients of number triangle A115284.

Links

Table of n, a(n) for n=0..50.

Index entries for linear recurrences with constant coefficients, signature (2,-1).

Formula

G.f.: (1+8*x+7*x^2)/(1-x)^2.

a(n) = 7*0^n + 2*(8*n-3).

a(n) = sum{k=0..n, (4-C(1, k)-2*C(0, k))^2}.

a(n) = A115284(2n, n).

a(0)=1, a(1)=10, a(2)=26, a(n) = 2*a(n-1)-a(n-2). [Harvey P. Dale, Aug 19 2011]

Mathematica

Accumulate[CoefficientList[Series[(1+x)^2/(1-x), {x, 0, 110}], x]^2] (* or *) Join[{1}, LinearRecurrence[{2, -1}, {10, 26}, 110]] (* Harvey P. Dale, Aug 19 2011 *)

Prog

(PARI) Vec((1+8*x+7*x^2)/(1-x)^2 + O(x^80)) \\ Michel Marcus, Feb 12 2016
(Magma) I:=[1, 10, 26]; [n le 3 select I[n] else 2*Self(n-1)-Self(n-2): n in [1..60]]; // Vincenzo Librandi, Feb 12 2016

Crossrefs

Sequence in context: A044071 A186279 A054315 * A223451 A229309 A044452

Adjacent sequences: A113767 A113768 A113769 * A113771 A113772 A113773

Keyword

easy,nonn

Author

Paul Barry, Jan 19 2006

Status

approved