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

1,5

Links

Table of n, a(n) for n=1..38.

Eric Weisstein's World of Mathematics, Graph Cycle

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

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.

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]

Crossrefs

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

Sequence in context: A041433 A222764 A058014 * A261785 A331013 A362283

Adjacent sequences: A290389 A290390 A290391 * A290393 A290394 A290395

Keyword

nonn,easy

Author

Eric W. Weisstein, Jul 29 2017

Status

approved