A295905 Number of (not necessarily maximal) cliques in the n X n knight graph.

2, 5, 18, 41, 74, 117, 170, 233, 306, 389, 482, 585, 698, 821, 954, 1097, 1250, 1413, 1586, 1769, 1962, 2165, 2378, 2601, 2834, 3077, 3330, 3593, 3866, 4149, 4442, 4745, 5058, 5381, 5714, 6057, 6410, 6773, 7146, 7529, 7922, 8325, 8738, 9161, 9594, 10037, 10490, 10953

Offset

1,1

Links

Table of n, a(n) for n=1..48.

Eric Weisstein's World of Mathematics, Clique

Eric Weisstein's World of Mathematics, Knight Graph

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

Formula

a(n) = 5*n^2 - 12*n + 9.

a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3).

G.f.: x*(-2 + x - 9 x^2)/(-1 + x)^3.

Mathematica

Table[5 n^2 - 12 n + 9, {n, 20}]
LinearRecurrence[{3, -3, 1}, {2, 5, 18}, 20]
CoefficientList[Series[(-2 + x - 9 x^2)/(-1 + x)^3, {x, 0, 20}], x]

Crossrefs

Sequence in context: A355515 A048221 A183365 * A056296 A293964 A275079

Adjacent sequences: A295902 A295903 A295904 * A295906 A295907 A295908

Keyword

nonn,easy

Author

Eric W. Weisstein, Nov 29 2017

Status

approved