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%I #24 Apr 05 2020 02:28:44
%S 2,13,101,619,3641,20028,106812,554352,2828660,14244878,71077246,
%T 352184306,1736118578,8525182798,41741378126,203929434766,
%U 994680883360,4845761306611,23586192274443,114731539477465,557859497501007,2711772157178038,13180227306740726
%N Number of polyhexes of class PF2 with four catafusenes annealated to pyrene.
%C See reference for precise definition.
%H S. J. Cyvin, Zhang Fuji, B. N. Cyvin, Guo Xiaofeng, and J. Brunvoll, <a href="https://doi.org/10.1021/ci00009a021">Enumeration and classification of benzenoid systems. 32. Normal perifusenes with two internal vertices</a>, J. Chem. Inform. Comput. Sci., 32 (1992), 532-540.
%H Sean A. Irvine, <a href="https://github.com/archmageirvine/joeis/blob/master/src/irvine/oeis/a030/A030519.java">Java program</a> (github)
%F 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
%o (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
%o 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
%o N(n) = polcoeff( (1 - x - sqrt(1 - 6*x + 5*x^2 + x^2 * O(x^n))) / 2, n+1); \\ A002212
%o 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;
%o a(n) = b(n-4); \\ _Michel Marcus_, Apr 03 2020
%Y Cf. A026106, A026118, A026298, A030519, A030520, A030525, A030529, A030532, A030534.
%K nonn
%O 8,1
%A _N. J. A. Sloane_
%E More terms and title improved by _Sean A. Irvine_, Apr 02 2020
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