A030435 Expansion of g.f. (1 + x - 2*x^2 - x^3)/(1/2 - 2*x^2 + x^4).

2, 2, 4, 6, 12, 20, 40, 68, 136, 232, 464, 792, 1584, 2704, 5408, 9232, 18464, 31520, 63040, 107616, 215232, 367424, 734848, 1254464, 2508928, 4283008, 8566016, 14623104, 29246208, 49926400, 99852800, 170459392, 340918784, 581984768, 1163969536, 1987020288

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Comments

Also (starting 4,6,...) the number of zig-zag paths from top to bottom of a rectangle of width 7, whose color is that of the top right corner. - Joseph Myers, Dec 24 2008

Links

• Harvey P. Dale, Table of n, a(n) for n = 0..1000
• Joseph Myers, BMO 2008--2009 Round 1 Problem 1---Generalisation
• Index entries for linear recurrences with constant coefficients, signature (0,4,0,-2).

Crossrefs

Twice A030436.

Programs

Mathematica

CoefficientList[Series[(1+x-2*x^2-x^3)/(1/2-2*x^2+x^4),{x,0,40}],x] (* Harvey P. Dale, Oct 05 2020 *)

PARI

Vec((1+x-2*x^2-x^3)/(1/2-2*x^2+x^4)+O(x^99)) \\ Charles R Greathouse IV, Sep 27 2012

Formula

E.g.f.: cosh(r*x) + cosh(s*x) + (r*sinh(r*x) + s*sinh(s*x))/2, where r = sqrt(2 - sqrt(2)) and s = sqrt(2 + sqrt(2)). - Stefano Spezia, Jun 14 2023