[go: up one dir, main page]

login
A295905
Number of (not necessarily maximal) cliques in the n X n knight graph.
0
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
Eric Weisstein's World of Mathematics, Clique
Eric Weisstein's World of Mathematics, Knight Graph
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
KEYWORD
nonn,easy
AUTHOR
Eric W. Weisstein, Nov 29 2017
STATUS
approved