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
Examples
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).
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).
Crossrefs
Cf. A131948.
Programs
-
Mathematica
LinearRecurrence[{5,-9,7,-2},{1,6,16,32},30] (* Harvey P. Dale, Feb 24 2016 *) -
PARI
Vec((1 + x - 5*x^2 - x^3) / ((1 - x)^3*(1 - 2*x)) + O(x^40)) \\ Colin Barker, Nov 04 2017
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)