A290392 Number of 6-cycles in the n-triangular honeycomb obtuse knight graph.

0, 0, 0, 0, 4, 13, 98, 415, 1151, 2471, 4385, 6893, 9995, 13691, 17981, 22865, 28343, 34415, 41081, 48341, 56195, 64643, 73685, 83321, 93551, 104375, 115793, 127805, 140411, 153611, 167405, 181793, 196775, 212351, 228521, 245285, 262643, 280595

Offset: 1

Author

Eric W. Weisstein, Jul 29 2017

Keywords

• nonn
• easy

Links

• Eric Weisstein's World of Mathematics, Graph Cycle
• Index entries for linear recurrences with constant coefficients, signature (3, -3, 1).

Crossrefs

Cf. A001105 (3-cycles in the triangular honeycomb obtuse knight graph), A194715 (4-cycles), A290391 (5-cycles).

Programs

Mathematica

Table[Piecewise[{{0, n <= 4}, {4, n == 5}, {13, n == 6}, {98, n == 7}, {415, n == 8}, {16001 - 4323 n + 297 n^2, n > 8}}, 0], {n, 20}]
Join[{0, 0, 0, 0, 4, 13, 98, 415}, LinearRecurrence[{3, -3, 1}, {1151, 2471, 4385}, 12]]
CoefficientList[Series[(x^4 (-4 - x - 71 x^2 - 156 x^3 - 187 x^4 - 165 x^5 - 10 x^6))/(-1 + x)^3, {x, 0, 20}], x]

Formula

For n >= 9, a(n) = 16001 - 4323*n + 297*n^2.

For n >= 12, a(n) = 3*a(n-1)-3*a(n-2)+a(n-3).

G.f.: x^5*(-4 - x - 71*x^2 - 156*x^3 - 187*x^4 - 165*x^5 - 10*x^6)/(-1 +

x)^3.