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A131949 Row sums of triangle A131948. 2
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 (list; graph; refs; listen; history; text; internal format)
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 * A243763 A061235 A239358

Adjacent sequences:  A131946 A131947 A131948 * A131950 A131951 A131952

KEYWORD

nonn,easy

AUTHOR

Gary W. Adamson, Jul 30 2007

STATUS

approved

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Last modified July 8 04:16 EDT 2020. Contains 335504 sequences. (Running on oeis4.)