A030519 Number of polyhexes of class PF2 with four catafusenes annealated to pyrene.

2, 13, 101, 619, 3641, 20028, 106812, 554352, 2828660, 14244878, 71077246, 352184306, 1736118578, 8525182798, 41741378126, 203929434766, 994680883360, 4845761306611, 23586192274443, 114731539477465, 557859497501007, 2711772157178038, 13180227306740726

Offset: 8

Author

N. J. A. Sloane

Keywords

• nonn

Comments

See reference for precise definition.

Links

• S. J. Cyvin, Zhang Fuji, B. N. Cyvin, Guo Xiaofeng, and J. Brunvoll, Enumeration and classification of benzenoid systems. 32. Normal perifusenes with two internal vertices, J. Chem. Inform. Comput. Sci., 32 (1992), 532-540.
• Sean A. Irvine, Java program (github)

Crossrefs

Cf. A026106, A026118, A026298, A030519, A030520, A030525, A030529, A030532, A030534.

Programs

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;
a(n) = b(n-4); \\ Michel Marcus, Apr 03 2020

Formula

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

Extensions

More terms and title improved by Sean A. Irvine, Apr 02 2020