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A030519
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Number of polyhexes of class PF2 with four catafusenes annealated to pyrene.
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9
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2, 13, 101, 619, 3641, 20028, 106812, 554352, 2828660, 14244878, 71077246, 352184306, 1736118578, 8525182798, 41741378126, 203929434766, 994680883360, 4845761306611, 23586192274443, 114731539477465, 557859497501007, 2711772157178038, 13180227306740726
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OFFSET
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8,1
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COMMENTS
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See reference for precise definition.
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LINKS
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FORMULA
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a(n+4) = N(n+3) - 9*N(n+2) + 25*N(n+1) - 21*N(n) + (M(n+3) - M(n+2) - 3*M(n+1) + 3*M(n) + L'(n))/2 where N(n)=A002212(n), M(n)=A055879(n), and L'(n)=A039660(n) for n >= 4. - Sean A. Irvine, Apr 02 2020
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PROG
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(PARI) Lp(n)=my(x = 'x + O('x^(n+4))); polcoeff((1+x)*(1-6*x^2+7*x^4-(1-3*x^2)*sqrt(1-6*x^2+5*x^4))/(2*x^4*(1-x)), n); \\ A039660
M(n)= my(A); if( n<1, 0, n--; A = O(x); for( k = 0, n\2, A = 1 / (1 - x - x^2 / (1 + x - x^2 * A))); polcoeff( A, n)); \\ A055879
N(n) = polcoeff( (1 - x - sqrt(1 - 6*x + 5*x^2 + x^2 * O(x^n))) / 2, n+1); \\ A002212
b(n) = N(n+3) - 9*N(n+2) + 25*N(n+1) - 21*N(n) + (M(n+3) - M(n+2) - 3*M(n+1) + 3*M(n) + Lp(n))/2;
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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