A199935 Size (b^3_n) of unit sphere in a certain graph (see Hazama article for precise definition).

0, 0, 2, 5, 9, 14, 22, 36, 60, 99, 161, 260, 420, 680, 1102, 1785, 2889, 4674, 7562, 12236, 19800, 32039, 51841, 83880, 135720, 219600, 355322, 574925, 930249, 1505174, 2435422, 3940596, 6376020, 10316619, 16692641, 27009260, 43701900, 70711160, 114413062, 185124225

Offset

2,3

Links

Vincenzo Librandi, Table of n, a(n) for n = 2..1000

Fumio Hazama, Spectra of graphs attached to the space of melodies, Discr. Math., 311 (2011), 2368-2383. See Table 2.1.

Index entries for linear recurrences with constant coefficients, signature (3,-3,1,1,-1).

Formula

a(n) = 2*A130578(n-1) - A130578(n-2).

G.f.: -x^4*(-2+x) / ( (x-1)*(x^2-x+1)*(x^2+x-1) ). - R. J. Mathar, Nov 15 2011

a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) + a(n-4) - a(n-5), with a(2)=0, a(3)=0, a(4)=2, a(5)=5, a(6)=9. - Harvey P. Dale, Jul 04 2013

Mathematica

CoefficientList[Series[-x^2*(-2+x)/((x-1)*(x^2-x+1)*(x^2+x-1)), {x, 0, 50}], x] (* Vincenzo Librandi, Jul 10 2012 *)
LinearRecurrence[{3, -3, 1, 1, -1}, {0, 0, 2, 5, 9}, 40] (* Harvey P. Dale, Jul 04 2013 *)

Crossrefs

Sequence in context: A306674 A098065 A123690 * A090937 A338666 A325717

Adjacent sequences: A199932 A199933 A199934 * A199936 A199937 A199938

Keyword

nonn,easy

Author

N. J. A. Sloane, Nov 12 2011

Status

approved