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A030519 Number of polyhexes of class PF2 with four catafusenes annealated to pyrene. 9
2, 13, 101, 619, 3641, 20028, 106812, 554352, 2828660, 14244878, 71077246, 352184306, 1736118578, 8525182798, 41741378126, 203929434766, 994680883360, 4845761306611, 23586192274443, 114731539477465, 557859497501007, 2711772157178038, 13180227306740726 (list; graph; refs; listen; history; text; internal format)
OFFSET

8,1

COMMENTS

See reference for precise definition.

LINKS

Table of n, a(n) for n=8..30.

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)

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

PROG

(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

CROSSREFS

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

Sequence in context: A064325 A123619 A187746 * A141116 A330349 A234299

Adjacent sequences:  A030516 A030517 A030518 * A030520 A030521 A030522

KEYWORD

nonn

AUTHOR

N. J. A. Sloane

EXTENSIONS

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

STATUS

approved

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Last modified July 3 10:20 EDT 2020. Contains 335417 sequences. (Running on oeis4.)