A295906 Number of (not necessarily maximal) cliques in the n X n king graph.

2, 16, 50, 104, 178, 272, 386, 520, 674, 848, 1042, 1256, 1490, 1744, 2018, 2312, 2626, 2960, 3314, 3688, 4082, 4496, 4930, 5384, 5858, 6352, 6866, 7400, 7954, 8528, 9122, 9736, 10370, 11024, 11698, 12392, 13106, 13840, 14594, 15368, 16162, 16976, 17810, 18664, 19538

Offset

1,1

Links

Table of n, a(n) for n=1..45.

Eric Weisstein's World of Mathematics, Clique

Eric Weisstein's World of Mathematics, King Graph

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

Formula

a(n) = 2*(5*n^2 - 8*n + 4).

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

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

Mathematica

Table[2 (5 n^2 - 8 n + 4), {n, 20}]
LinearRecurrence[{3, -3, 1}, {2, 16, 50}, 20]
CoefficientList[Series[-2 (1 + 5 x + 4 x^2)/(-1 + x)^3, {x, 0, 20}], x]

Crossrefs

Sequence in context: A232209 A012180 A058376 * A120948 A090453 A006885

Adjacent sequences: A295903 A295904 A295905 * A295907 A295908 A295909

Keyword

nonn,easy

Author

Eric W. Weisstein, Nov 29 2017

Status

approved