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A121135 Numbers of isomers of unbranched a-4-catapolypentagons - see Brunvoll reference for precise definition. 1
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

3,2

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=3..30.

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

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Last modified January 22 15:13 EST 2022. Contains 350481 sequences. (Running on oeis4.)