A216263 Expansion of 1 / ((1-2*x)*(1-4*x+x^2)).
1, 6, 27, 110, 429, 1638, 6187, 23238, 87021, 325358, 1215435, 4538430, 16942381, 63239286, 236031147, 880918070, 3287706669, 12270039678, 45792714187, 170901341358, 637813699821, 2380355555078, 8883612714795, 33154103692710, 123732818833261, 461777205194766, 1723376069054667
Offset: 0
Links
- Colin Barker, Table of n, a(n) for n = 0..1000
- László Németh and László Szalay, Sequences Involving Square Zig-Zag Shapes, J. Int. Seq., Vol. 24 (2021), Article 21.5.2.
- Index entries for linear recurrences with constant coefficients, signature (6,-9,2).
Programs
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Mathematica
CoefficientList[Series[1/((1 - 2 x)*(1 - 4 x + x^2)), {x, 0, 26}], x] (* Michael De Vlieger, Aug 05 2021 *) -
PARI
Vec(1/((1-2*x)*(1-4*x+x^2)) + O(x^30)) \\ Colin Barker, Feb 05 2017
Formula
G.f.: 1/((1-2*x)*(1-4*x+x^2)).
a(n) = 6*a(n-1) - 9*a(n-2) + 2*a(n-3), a(0) = 1, a(1) = 6, a(2) = 27.
3*a(n) = -2^(n+2) + A001075(n+2). - R. J. Mathar, Mar 29 2013
a(n) = (-2^(3+n) + (7-4*sqrt(3))*(2-sqrt(3))^n + (2+sqrt(3))^n*(7+4*sqrt(3))) / 6. - Colin Barker, Feb 05 2017