A234272 G.f.: (1+4*x+x^2)/(1-4*x+x^2).

1, 8, 32, 120, 448, 1672, 6240, 23288, 86912, 324360, 1210528, 4517752, 16860480, 62924168, 234836192, 876420600, 3270846208, 12206964232, 45557010720, 170021078648, 634527303872, 2368088136840, 8837825243488, 32983212837112, 123095026104960, 459396891582728, 1714492540225952, 6398573269321080

Offset

0,2

Links

Colin Barker, Table of n, a(n) for n = 0..1000

J. Choi, N. Pippenger, Counting the Angels and Devils in Escher's Circle Limit IV, arXiv preprint arXiv:1310.1357, 2013

Index entries for linear recurrences with constant coefficients, signature (4,-1).

Formula

a(n) = 8*A001353(n), n>0. - R. J. Mathar, Jan 21 2014

From Colin Barker, Oct 12 2015: (Start)

a(n) = 4*a(n-1)-a(n-2) for n>2.

a(n) = 4*(-(2-sqrt(3))^n+(2+sqrt(3))^n)/sqrt(3) for n>1.

(End)

Mathematica

CoefficientList[Series[(1+4x+x^2)/(1-4x+x^2), {x, 0, 30}], x] (* or *) LinearRecurrence[{4, -1}, {1, 8, 32}, 30] (* Harvey P. Dale, Jul 12 2015 *)

Prog

(PARI) Vec((1+4*x+x^2)/(1-4*x+x^2) + O(x^40)) \\ Colin Barker, Oct 12 2015

Crossrefs

Sequence in context: A003201 A318944 A196097 * A269077 A183915 A357789

Adjacent sequences: A234269 A234270 A234271 * A234273 A234274 A234275

Keyword

nonn,easy

Author

N. J. A. Sloane, Dec 24 2013

Status

approved