A121135 Numbers of isomers of unbranched a-4-catapolypentagons - see Brunvoll reference for precise definition.

1, 2, 8, 22, 74, 208, 598, 1600, 4248, 10880, 27512, 68096, 166528, 401408, 957728, 2260992, 5292672, 12288000, 28329344, 64880640, 147721216, 334495744, 753670656, 1690304512, 3774887936, 8396996608, 18610157568, 41104179200

Offset

3,2

Links

Table of n, a(n) for n=3..30.

J. Brunvoll, S. J. Cyvin, and B. N. Cyvin, Isomer enumeration of polygonal systems..., J. Molec. Struct. (Theochem), 364 (1996), 1-13.

Index entries for linear recurrences with constant coefficients, signature (8,-20,0,76,-96,-32,128,-64).

Formula

G.f.: x^3 * (16*x^10-40*x^8+8*x^7+30*x^6-18*x^4-2*x^3+12*x^2-6*x+1) / ((2*x-1)^4 * (2*x^2-1)^2). - Colin Barker, Nov 30 2012

Maple

H := proc(r, alpha, q) local rhalf, alphahalf ; rhalf := floor(r/2) ; alphahalf := floor(alpha/2) ; (binomial(rhalf-1, alphahalf-1)*(q-3)+binomial(rhalf-1, alphahalf))*(q-3)^(rhalf-alphahalf-1) ; end: J := proc(r, alpha, q) (binomial(r-2, alpha-2)*(q-3)^2+2*binomial(r-2, alpha-1)*(q-3)+binomial(r-2, alpha))*(q-3)^(r-alpha-2) ; end: Ifunc := proc(r, alpha, q) J(r, alpha, q)/4+binomial(2, r-alpha)/4+ (1+(-1)^(r+alpha)+(1+(-1)^alpha)*(1-(-1)^r)/2)*H(r, alpha, q)/4 ; end: A121135 := proc(n) Ifunc(n, 3, 5) ; end: for n from 3 to 80 do printf("%d, ", A121135(n)) ; od: # R. J. Mathar, Aug 07 2008

Crossrefs

Cf. A121133. - R. J. Mathar, Aug 07 2008

Sequence in context: A339302 A045695 A106053 * A183410 A072929 A328140

Adjacent sequences: A121132 A121133 A121134 * A121136 A121137 A121138

Keyword

nonn,easy

Author

N. J. A. Sloane, Aug 13 2006

Extensions

Extended beyond a(10) by R. J. Mathar, Aug 07 2008

Status

approved