A048514 a(n) = T(0,n)+T(1,n-1)+...+T(n,0), array T given by A048505.

1, 3, 13, 54, 190, 587, 1659, 4412, 11244, 27785, 67089, 159106, 371930, 859159, 1964855, 4454968, 10025240, 22411221, 49804909, 110097630, 242217766, 530575683, 1157623603, 2516577524, 5452589700, 11777599457

Offset

0,2

Links

Table of n, a(n) for n=0..25.

Index entries for linear recurrences with constant coefficients, signature (10,-42,96, -129,102,-44,8).

Formula

G.f.: (8*x^5-37*x^4+46*x^3-25*x^2+7*x-1) / ((x-1)^4*(2*x-1)^3). - Colin Barker, Feb 25 2015

Mathematica

LinearRecurrence[{10, -42, 96, -129, 102, -44, 8}, {1, 3, 13, 54, 190, 587, 1659}, 30] (* Harvey P. Dale, Aug 01 2022 *)

Prog

(PARI)
T(k, n) = (n^2 + (4*k+1)*n + (2*k)^2) * 2^(n-2) - k^2 + 1
a(n) = sum(k=0, n, T(k, n-k)) \\ Colin Barker, Feb 25 2015

Crossrefs

Sequence in context: A065839 A066611 A180933 * A037779 A323264 A362495

Adjacent sequences: A048511 A048512 A048513 * A048515 A048516 A048517

Keyword

nonn

Author

Clark Kimberling

Extensions

Typo in a(25) fixed by Colin Barker, Feb 25 2015

Status

approved