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%I #14 Aug 12 2015 01:57:31
%S 1,2,8,22,74,208,598,1600,4248,10880,27512,68096,166528,401408,957728,
%T 2260992,5292672,12288000,28329344,64880640,147721216,334495744,
%U 753670656,1690304512,3774887936,8396996608,18610157568,41104179200
%N Numbers of isomers of unbranched a-4-catapolypentagons - see Brunvoll reference for precise definition.
%D J. Brunvoll, S. J. Cyvin and B. N. Cyvin, Isomer enumeration of polygonal systems..., J. Molec. Struct. (Theochem), 364 (1996), 1-13.
%H <a href="/index/Rec">Index entries for linear recurrences with constant coefficients</a>, signature (8,-20,0,76,-96,-32,128,-64).
%F 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
%p 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
%Y Cf. A121133. - _R. J. Mathar_, Aug 07 2008
%K nonn,easy
%O 3,2
%A _N. J. A. Sloane_, Aug 13 2006
%E Extended beyond a(10) by _R. J. Mathar_, Aug 07 2008
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