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

0,2

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).

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

Mathematica

CoefficientList[Series[1/((1 - 2 x)*(1 - 4 x + x^2)), {x, 0, 26}], x] (* Michael De Vlieger, Aug 05 2021 *)

Prog

(PARI) Vec(1/((1-2*x)*(1-4*x+x^2)) + O(x^30)) \\ Colin Barker, Feb 05 2017

Crossrefs

A diagonal of A214846.

Cf. A001075.

Sequence in context: A022634 A094788 A221863 * A003517 A108958 A005284

Adjacent sequences: A216260 A216261 A216262 * A216264 A216265 A216266

Keyword

nonn,easy

Author

Philippe Deléham, Mar 15 2013

Status

approved