A030529 Number of polyhexes of class PF2 with a particular symmetry.

0, 0, 1, 4, 17, 66, 269, 1102, 4635, 19768, 85659, 375524, 1664015, 7438862, 33515027, 152016610, 693622315, 3181516040, 14661568795, 67850245684, 315187594779, 1469195413102, 6869889480447, 32215398047474, 151467333043437, 713881813137776, 3372142135461789

Offset

2,4

Comments

See references for precise definition.

Column D_{2h}(b) and Eq. 50 in Cyvin et al. (1994). - Sean A. Irvine, Mar 27 2021

Links

Table of n, a(n) for n=2..28.

S. J. Cyvin, J. Brunvoll, and B. N. Cyvin, Harary-Read numbers for catafusenes: Complete classification according to symmetry, Journal of mathematical chemistry 9.1 (1992): 19-31 and 33-38. See pages 30 and 38.

S. J. Cyvin, B. N. Cyvin, J. Brunvoll and E. Brendsdal, Enumeration and Classification of Certain Polygonal Systems Representing Polycyclic Conjugated Hydrocarbons: Annelated Catafusenes, Journal of Chemical Information and Modeling [formerly, J. Chem. Inform. Comput. Sci.], 34 (1994), pp. 1174-1180.

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(2)=0, a(n+2) = (M(2*n+1) - M(2*n) - M(n)) / 2 where M(n) = A055879(n) [Cyvin Eq. (54)]. - Sean A. Irvine, Apr 03 2020

Prog

(PARI) A055879(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));
b(n) = (A055879(2*n+1) - A055879(2*n) - A055879(n)) / 2;
a(n) = if( n<=2, 0, b(n - 2)); \\ Michel Marcus, Apr 03 2020

Crossrefs

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

Sequence in context: A046723 A291394 A244616 * A266862 A239845 A081113

Adjacent sequences: A030526 A030527 A030528 * A030530 A030531 A030532

Keyword

nonn

Author

N. J. A. Sloane.

Extensions

More terms from Sean A. Irvine, Apr 03 2020

Status

approved