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

Author

Paul Barry, Jan 19 2006

Keywords

• easy
• nonn

Comments

Central coefficients of number triangle A115284.

Links

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

Programs

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

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 *)

PARI

Vec((1+8*x+7*x^2)/(1-x)^2 + O(x^80)) \\ Michel Marcus, Feb 12 2016

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]