A131949 Row sums of triangle A131948.

1, 6, 16, 32, 56, 92, 148, 240, 400, 692, 1244, 2312, 4408, 8556, 16804, 33248, 66080, 131684, 262828, 525048, 1049416, 2098076, 4195316, 8389712, 16778416, 33555732, 67110268, 134219240, 268437080, 536872652, 1073743684, 2147485632, 4294969408, 8589936836

Offset

0,2

Links

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

Index entries for linear recurrences with constant coefficients, signature (5,-9,7,-2).

Formula

Binomial transform of (1, 5, 5, 1, 1, 1, ...).

G.f.: 1-2*x*(-3+7*x-3*x^2+x^3) / ( (2*x-1)*(x-1)^3 ). - R. J. Mathar, Apr 04 2012

From Colin Barker, Nov 04 2017: (Start)

a(n) = 2^n + 2*n + 2*n^2.

a(n) = 5*a(n-1) - 9*a(n-2) + 7*a(n-3) - 2*a(n-4) for n > 3.

(End)

Example

a(3) = 32 = sum of row 3 terms, triangle A131948: (7 + 9 + 9 + 7).
a(3) = 32 = (1, 3, 3, 1) dot (1, 5, 5, 1) = (1 + 15 + 15 + 1).

Mathematica

LinearRecurrence[{5, -9, 7, -2}, {1, 6, 16, 32}, 30] (* Harvey P. Dale, Feb 24 2016 *)

Prog

(PARI) Vec((1 + x - 5*x^2 - x^3) / ((1 - x)^3*(1 - 2*x)) + O(x^40)) \\ Colin Barker, Nov 04 2017

Crossrefs

Cf. A131948.

Sequence in context: A301713 A134465 A036488 * A345023 A243763 A061235

Adjacent sequences: A131946 A131947 A131948 * A131950 A131951 A131952

Keyword

nonn,easy

Author

Gary W. Adamson, Jul 30 2007

Status

approved