A290391 Number of 5-cycles in the n-triangular honeycomb obtuse knight graph.

0, 0, 0, 0, 0, 0, 30, 120, 294, 552, 894, 1320, 1830, 2424, 3102, 3864, 4710, 5640, 6654, 7752, 8934, 10200, 11550, 12984, 14502, 16104, 17790, 19560, 21414, 23352, 25374, 27480, 29670, 31944, 34302, 36744, 39270, 41880, 44574, 47352, 50214, 53160, 56190, 59304, 62502

Offset

1,7

Links

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

Eric Weisstein's World of Mathematics, Graph Cycle

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

Formula

For n >= 7, a(n) = 6*(292 - 90*n + 7*n^2).

For n >= 10, a(n) = 3*a(n-1)-3*a(n-2)+a(n-3).

G.f.: -6*x^7*(5 + 5*x + 4*x^2)/(-1 + x)^3.

Mathematica

Table[If[n < 7, 0, 6 (292 - 90 n + 7 n^2)], {n, 20}]
Join[{0, 0, 0, 0, 0, 0}, LinearRecurrence[{3, -3, 1}, {30, 120, 294}, 14]]
CoefficientList[Series[-((6 x^6 (5 + 5 x + 4 x^2))/(-1 + x)^3), {x, 0, 20}], x]

Crossrefs

Cf. A001105 (3-cycles in the triangular honeycomb obtuse knight graph), A194715 (4-cycles), A290392 (6-cycles).

Sequence in context: A246766 A112955 A244636 * A277451 A042764 A219223

Adjacent sequences: A290388 A290389 A290390 * A290392 A290393 A290394

Keyword

nonn,easy

Author

Eric W. Weisstein, Jul 29 2017

Status

approved