A121134 Numbers of isomers of unbranched a-4-catapolypentagons - see Brunvoll reference for precise definition.

1, 2, 5, 11, 30, 72, 182, 434, 1048, 2456, 5752, 13240, 30336, 68736, 154912, 346400, 770688, 1704576, 3753344, 8226176, 17959936, 39062528, 84679168, 182983168, 394278912, 847263744, 1816164352, 3883956224, 8288010240, 17649696768

Offset

2,2

References

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

Links

Table of n, a(n) for n=2..31.

Index entries for linear recurrences with constant coefficients, signature (6,-8,-16,44,-8,-48,32).

Formula

G.f.: x*(8*x^9+4*x^8-18*x^7-10*x^6+20*x^5+8*x^4-13*x^3-x^2+4*x-1) / ((2*x-1)^3*(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: A121134 := proc(n) Ifunc(n, 2, 5) ; end: for n from 2 to 80 do printf("%d, ", A121134(n)) ; od: # R. J. Mathar, Aug 07 2008

Crossrefs

Sequence in context: A272675 A059075 A345882 * A144959 A131347 A292210

Adjacent sequences: A121131 A121132 A121133 * A121135 A121136 A121137

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