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A121136
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Numbers of isomers of unbranched a-4-catapolypentagons - see Brunvoll reference for precise definition.
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2
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1, 3, 13, 45, 164, 527, 1652, 4876, 14000, 38800, 105112, 278104, 722736, 1846320, 4650368, 11560320, 28413312, 69111168, 166551680, 397975680, 943672576, 2221821184, 5197313024, 12084884480, 27944656896, 64286203904, 147182565376
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OFFSET
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4,2
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REFERENCES
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J. Brunvoll, S. J. Cyvin and B. N. Cyvin, Isomer enumeration of polygonal systems..., J. Molec. Struct. (Theochem), 364 (1996), 1-13.
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LINKS
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Table of n, a(n) for n=4..30.
Index to sequences with linear recurrences with constant coefficients, signature (10,-34,20,148,-328,8,688,-640,-256,640,-256).
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FORMULA
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G.f.: x^4 * (64*x^13 -32*x^12 -192*x^11 +128*x^10 +212*x^9 -172*x^8 -114*x^7 +110*x^6 +41*x^5 -52*x^4 -3*x^3 +17*x^2 -7*x+1) / ((2*x-1)^5 * (2*x^2-1)^3). - Colin Barker, Nov 30 2012
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MAPLE
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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: A121136 := proc(n) Ifunc(n, 4, 5) ; end: for n from 4 to 80 do printf("%d, ", A121136(n)) ; od: # R. J. Mathar, Aug 07 2008
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CROSSREFS
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Cf. A121133. - R. J. Mathar, Aug 07 2008
Sequence in context: A187915 A115128 A140420 * A017943 A220117 A089930
Adjacent sequences: A121133 A121134 A121135 * A121137 A121138 A121139
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KEYWORD
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nonn,easy
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AUTHOR
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N. J. A. Sloane, Aug 13 2006
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EXTENSIONS
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Extended beyond a(10) by R. J. Mathar, Aug 07 2008
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STATUS
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approved
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