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

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy

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).

Programs

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 *)

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

Extensions

More terms from Colin Barker, Aug 30 2013