A038390 - OEIS

A038390

Bisection of A028289.

1, 2, 5, 11, 17, 27, 42, 57, 78, 106, 134, 170, 215, 260, 315, 381, 447, 525, 616, 707, 812, 932, 1052, 1188, 1341, 1494, 1665, 1855, 2045, 2255, 2486, 2717, 2970, 3246, 3522, 3822, 4147, 4472, 4823, 5201, 5579, 5985, 6420, 6855, 7320, 7816, 8312, 8840, 9401

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,2

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

B. N. Cyvin et al., Enumeration of conjugated hydrocarbons: Hollow hexagons revisited, Structural Chem., 6 (1995), 85-88, equation (7).

Index entries for linear recurrences with constant coefficients, signature (2,-1,2,-4,2,-1,2,-1).

FORMULA

G.f.: (x^3+2*x^2+1) / ((x-1)^4*(x^2+x+1)^2). - Colin Barker, Aug 30 2013

a(n) = (2*n^2+2+floor(n/3)*(10*floor(n/3)^2-(8*n-15)*floor(n/3)+2*n^2-8*n+7))/2. - Luce ETIENNE, Sep 14 2015

MATHEMATICA

CoefficientList[Series[(x^3 + 2 x^2 + 1)/((x - 1)^4 (x^2 + x + 1)^2), {x, 0, 50}], x] (* Vincenzo Librandi, Oct 22 2013 *)