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

Author

N. J. A. Sloane, Nov 12 2011

Keywords

• nonn
• easy

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).

Programs

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 *)

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