A222203 -id:A222203 - cp's OEIS frontend

A222202 Number of ways to cover the 2n X 2n grid graph by vertex disjoint cycles.

1, 18, 13903, 360783593, 303872744726644, 8217125138015950451626, 7095967027221343377167292602835, 195081705501438193439250404333039349462635, 170400931523966165754313513175663906434875251822099185, 4722705723996809689481769489662532396060449405036901391459114641198

Offset: 1

N. J. A. Sloane, Feb 14 2013

nonn

Andrew Howroyd, Table of n, a(n) for n = 1..12
Peter Tittmann, Enumeration in graphs: counting Hamiltonian cycles [Archived link]

Cf. A222203, A222204.

a(10)-a(12) from Andrew Howroyd, Nov 16 2015

A003693 Number of 2-factors in P_4 X P_n.

Original entry on oeis.org

0, 2, 3, 18, 54, 222, 779, 2953, 10771, 40043, 147462, 545603, 2013994, 7442927, 27490263, 101563680, 375176968, 1386004383, 5120092320, 18914660608, 69873991466, 258127586367, 953569519203, 3522660270539

Offset: 1

Frans J. Faase

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

Andrew Howroyd, Table of n, a(n) for n = 1..200
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
Index entries for linear recurrences with constant coefficients, signature (2, 7, -2, -3, 1).

Cf. A003776, A145400, A145415, A145417, A222202, A222203.

LinearRecurrence[{2, 7, -2, -3, 1}, {0, 2, 3, 18, 54}, 30] (* Jean-François Alcover, Sep 21 2019 *)

a(n) = 2a(n-1) + 7a(n-2) - 2a(n-3) - 3a(n-4) + a(n-5), n > 5.

G.f.: (-x*(x-1)*(x-2)*(x+1))/(-1 + x^5 - 3*x^4 - 2*x^3 + 7*x^2 + 2*x). - Maksym Voznyy (voznyy(AT)mail.ru), Aug 10 2009

A222204 Write n=3i+j, 0<=j<3; a(n) = number of ways to cover the r X s grid graph by vertex disjoint cycles, where (r,s) = (2i+2, 2i+2) (if j=0), (2i+2, 2i+3) (if j=1) or (2i+3, 2i+4) (if j=2).

Original entry on oeis.org

1, 1, 3, 18, 54, 1140, 13903, 99051, 13049563, 360783593, 6044482889, 4738211572702, 303872744726644, 11986520595161863, 54755153078468134960, 8217125138015950451626, 764291947227525464744293, 20119942924108379011391597989, 7095967027221343377167292602835, 1558052539448513320447263528275071

Offset: 0

N. J. A. Sloane, Feb 14 2013

nonn

An interleaving of A222202 and A222203.

Peter Tittmann, Enumeration in graphs: counting Hamiltonian cycles [Broken link?]
Peter Tittmann, Enumeration in graphs: counting Hamiltonian cycles [Backup copy of top page only, on the Internet Archive]

Cf. A222202, A222203.

cp's OEIS Frontend

A222202 Number of ways to cover the 2n X 2n grid graph by vertex disjoint cycles.

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A003693 Number of 2-factors in P_4 X P_n.

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A222204 Write n=3i+j, 0<=j<3; a(n) = number of ways to cover the r X s grid graph by vertex disjoint cycles, where (r,s) = (2i+2, 2i+2) (if j=0), (2i+2, 2i+3) (if j=1) or (2i+3, 2i+4) (if j=2).

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