A180583 Number of Hamiltonian cycles in C_7 X P_n.

1, 7, 126, 1484, 18452, 229698, 2861964, 35663964, 444486280, 5539931796, 69048910000, 860620499760, 10726732430288, 133697577587000, 1666401898058352, 20769976722986288, 258876295158900832

Offset

1,2

Links

Table of n, a(n) for n=1..17.

Artem M. Karavaev, FlowProblem.ru web-project: Hamilton Cycles page.

Index entries for linear recurrences with constant coefficients, signature (12,18,-112,-440,-772,-196,2064,3724,2040,496,128,-16).

Formula

a(1) = 1,

a(2) = 7,

a(3) = 126,

a(4) = 1484,

a(5) = 18452,

a(6) = 229698,

a(7) = 2861964,

a(8) = 35663964,

a(9) = 444486280,

a(10) = 5539931796,

a(11) = 69048910000,

a(12) = 860620499760,

a(13) = 10726732430288 and

a(n) = -16a(n-12) + 128a(n-11) + 496a(n-10) + 2040a(n-9) +

3724a(n-8) + 2064a(n-7) - 196a(n-6) - 772a(n-5) - 440a(n-4) -

112a(n-3) + 18a(n-2) + 12a(n-1), n>13.

G.f.: x*(16*x^12 -16*x^11 +8*x^10 -192*x^9 +588*x^8 +1996*x^7 +700*x^6 -474*x^5 -400*x^4 -42*x^3 +24*x^2 -5*x +1)/(16*x^12 -128*x^11 -496*x^10 -2040*x^9 -3724*x^8 -2064*x^7 +196*x^6 +772*x^5 +440*x^4 +112*x^3 -18*x^2 -12*x +1). [Colin Barker, Sep 01 2012]

Crossrefs

Cf. A003699, A003731, A180582, A180584, A180585, A180586, A180587, A180588.

Sequence in context: A316276 A220615 A113162 * A295412 A202798 A204248

Adjacent sequences: A180580 A180581 A180582 * A180584 A180585 A180586

Keyword

nonn,easy

Author

Artem M. Karavaev, Sep 10 2010

Status

approved