A288917 Number of 6-cycles in the n X n queen graph.

0, 0, 976, 26414, 207136, 951750, 3190304, 8721576, 20615340, 43736788, 85332868, 155691014, 268995384, 444000894, 705336724, 1083967932, 1619250600, 2358809948, 3361809572, 4697700286, 6451359236, 8719953330, 11620829368

Offset

1,3

Links

Table of n, a(n) for n=1..23.

Eric Weisstein's World of Mathematics, Graph Cycle

Eric Weisstein's World of Mathematics, Queen Graph

Index entries for linear recurrences with constant coefficients, signature (0, 3, 2, -1, -5, -6, -1, 6, 11, 6, -4, -10, -10, -4, 6, 11, 6, -1, -6, -5, -1, 2, 3, 0, -1).

Formula

a(n)=3*a(n-2)+2*a(n-3)-a(n-4)-5*a(n-5)-6*a(n-6)-a(n-7)+6*a(n-8)+11*a(n-9)+6*a(n-10)-4*a(n-11)-10*a(n-12)-10*a(n-13)-4*a(n-14)+6*a(n-15)+11*a(n-16)+6*a(n-17)-a(n-18)-6*a(n-19)-5*a(n-20)-a(n-21)+2*a(n-22)+3*a(n-23)-a(n-25).

Mathematica

LinearRecurrence[{0, 3, 2, -1, -5, -6, -1, 6, 11, 6, -4, -10, -10, -4, 6, 11, 6, -1, -6, -5, -1, 2, 3, 0, -1}, {0, 0, 976, 26414, 207136, 951750, 3190304, 8721576, 20615340, 43736788, 85332868, 155691014, 268995384, 444000894, 705336724, 1083967932, 1619250600, 2358809948, 3361809572, 4697700286, 6451359236, 8719953330, 11620829368, 15285494276, 19871396864}, 30]

Crossrefs

Cf. A144298 (3-cycles), A156001 (4-cycles), A288916 (5-cycles).

Sequence in context: A233984 A205252 A190400 * A264130 A282405 A077362

Adjacent sequences: A288914 A288915 A288916 * A288918 A288919 A288920

Keyword

nonn,easy

Author

Eric W. Weisstein, Jun 19 2017

Status

approved