A048481 a(n) = T(0,n) + T(1,n-1) + ... + T(n,0), array T given by A048472.

1, 3, 9, 27, 77, 207, 529, 1299, 3093, 7191, 16409, 36891, 81949, 180255, 393249, 852003, 1835045, 3932199, 8388649, 17825835, 37748781, 79691823, 167772209, 352321587, 738197557, 1543503927, 3221225529, 6710886459, 13958643773, 28991029311, 60129542209

Offset

0,2

Links

Colin Barker, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (6,-13,12,-4).

Formula

Row sums of triangle A134397. Also, binomial transform of A048166. - Gary W. Adamson, Oct 23 2007

From Colin Barker, Dec 04 2014: (Start)

a(n) = 6*a(n-1) - 13*a(n-2) + 12*a(n-3) - 4*a(n-4).

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

a(n) = 2^(n+1)*(n-2) + 2*n + 5. - Christian Krause, Oct 31 2023

E.g.f.: exp(x)*(4*exp(x)*(x-1) + (2*x+5)). - Elmo R. Oliveira, Oct 25 2025

Mathematica

LinearRecurrence[{6, -13, 12, -4}, {1, 3, 9, 27}, 40] (* Harvey P. Dale, Aug 13 2015 *)

Prog

(PARI) Vec((4*x^2-3*x+1)/((x-1)^2*(2*x-1)^2) + O(x^100)) \\ Colin Barker, Dec 04 2014

Crossrefs

Partial sums of A048495.

Cf. A048166, A048472, A134397.

Sequence in context: A135415 A182897 A228734 * A269488 A027027 A361845

Adjacent sequences: A048478 A048479 A048480 * A048482 A048483 A048484

Keyword

nonn,easy

Author

Clark Kimberling

Extensions

Corrected by T. D. Noe, Nov 08 2006

Status

approved