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A289181 Number of 6-cycles in the n X n knight graph. 1
0, 0, 0, 20, 164, 616, 1348, 2352, 3628, 5176, 6996, 9088, 11452, 14088, 16996, 20176, 23628, 27352, 31348, 35616, 40156, 44968, 50052, 55408, 61036, 66936, 73108, 79552, 86268, 93256, 100516, 108048, 115852, 123928, 132276, 140896, 149788, 158952, 168388, 178096 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,4

LINKS

Table of n, a(n) for n=1..40.

Eric Weisstein's World of Mathematics, Graph Cycle

Eric Weisstein's World of Mathematics, Knight Graph

Index entries for linear recurrences with constant coefficients, signature (3, -3, 1).

FORMULA

For n > 5, a(n) = 4 (34 n^2 - 259 n + 484).

G.f.: (4*x^4*(-5 - 26*x - 46*x^2 + 7*x^3 + 2*x^4))/(-1 + x)^3.

MATHEMATICA

Table[Length[FindCycle[KnightTourGraph[n, n], {6}, All]], {n, 20}]

Table[Piecewise[{{0, n < 4}, {20, n == 4}, {164, n == 5}}, 4 (34 n^2 - 259 n + 484)], {n, 20}]

Join[{0, 0, 0, 20, 164}, LinearRecurrence[{3, -3, 1}, {1036, 408, 52}, {6, 20}]]

CoefficientList[Series[(4 x^3 (-5 - 26 x - 46 x^2 + 7 x^3 + 2 x^4))/(-1 + x)^3, {x, 0, 20}], x]

CROSSREFS

Cf. A163433 (4-cycles).

Sequence in context: A067534 A041768 A221870 * A056114 A281204 A186259

Adjacent sequences:  A289178 A289179 A289180 * A289182 A289183 A289184

KEYWORD

nonn

AUTHOR

Eric W. Weisstein, Jun 27 2017

STATUS

approved

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Last modified March 20 19:52 EDT 2019. Contains 321349 sequences. (Running on oeis4.)