A003744 Number of Hamiltonian paths in O_5 X P_n.

36, 3960, 197172, 8372376, 313590732, 10961493288, 364496212992, 11715923002644, 367218115613412, 11297962590845364, 342721436917704060, 10284809936813182116, 306078425919342660924

Offset: 1

Author

Frans J. Faase

Keywords

• nonn

References

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

Links

• Sean A. Irvine, Table of n, a(n) for n = 1..100
• 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

a(1) = 36,

a(2) = 3960,

a(3) = 197172,

a(4) = 8372376,

a(5) = 313590732,

a(6) = 10961493288,

a(7) = 364496212992,

a(8) = 11715923002644,

a(9) = 367218115613412,

a(10) = 11297962590845364,

a(11) = 342721436917704060,

a(12) = 10284809936813182116,

a(13) = 306078425919342660924,

a(14) = 9050314137435866812308,

a(15) = 266262758895847900204044,

a(16) = 7802857128214786920966468,

a(17) = 227964188131745757879553596,

a(18) = 6644168196971243295712163700,

a(19) = 193287318120848681996183075244,

a(20) = 5614785173559337471057013732388,

a(21) = 162918194408431653609336890189340,

a(22) = 4723043996602440520832973512325972,

a(23) = 136828273928341927052870400623002380, and

a(n) = 59a(n-1) - 731a(n-2) - 11403a(n-3) + 204688a(n-4) + 697232a(n-5)

- 13575824a(n-6) + 15466532a(n-7) + 288258520a(n-8) - 1327022000a(n-9) + 1631290560a(n-10)

+ 3212771840a(n-11) - 12023726208a(n-12) + 9649896000a(n-13) + 11298643072a(n-14) - 24109594624a(n-15)

+ 6239014400a(n-16) + 14028280832a(n-17) - 8564428800a(n-18) - 2763866112a(n-19) + 2175729664a(n-20)

+ 199229440a(n-21) - 150994944a(n-22).

Extensions

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