A003732 Number of Hamiltonian paths in C_5 X P_n.

5, 130, 1660, 16820, 152230, 1275680, 10154290, 77897010, 581452680, 4250594690, 30572999140, 217099260110, 1525905283670, 10636695448300, 73649615037480, 507171127397480, 3476871213780220, 23747634842538120

Offset

1,1

References

F. Faase, On the number of specific spanning subgraphs of the graphs G X P_n, Ars Combin. 49 (1998), 129-154.

Links

Table of n, a(n) for n=1..18.

F. Faase, On the number of specific spanning subgraphs of the graphs G X P_n, Preliminary version of paper that appeared in Ars Combin. 49 (1998), 129-154.

F. Faase, Counting Hamiltonian cycles in product graphs

F. Faase, Results from the counting program

Formula

Faase gives a 12-term linear recurrence on his web page:

a(1) = 5,

a(2) = 130,

a(3) = 1660,

a(4) = 16820,

a(5) = 152230,

a(6) = 1275680,

a(7) = 10154290,

a(8) = 77897010,

a(9) = 581452680,

a(10) = 4250594690,

a(11) = 30572999140,

a(12) = 217099260110,

a(13) = 1525905283670,

a(14) = 10636695448300 and

a(n) = 19a(n-1) - 127a(n-2) + 328a(n-3) - 117a(n-4) - 675a(n-5)

+ 1127a(n-6) - 1016a(n-7) + 380a(n-8) + 12a(n-9) - 140a(n-10)

+ 68a(n-11) - 20a(n-12), n>14.

G.f. 5*x+130*x^2 -10*x^3*(-166 +1472*x -4347*x^2 +2503*x^3 +7316*x^4 -13386*x^5 +12513*x^6 -4715*x^7 -215*x^8 +1824*x^9 -856*x^10 +252*x^11) / ( (1-7*x-x^2+20*x^3-3*x^4+3*x^5+5*x^6) *(-1+6*x-4*x^2+2*x^3)^2 ). - R. J. Mathar, Aug 21 2012

Crossrefs

Sequence in context: A281818 A332317 A069078 * A203476 A203702 A142892

Adjacent sequences: A003729 A003730 A003731 * A003733 A003734 A003735

Keyword

nonn

Author

Frans J. Faase

Extensions

Added recurrence from Faase's web page. - N. J. A. Sloane, Feb 03 2009

Status

approved