A290940 Number of 6-cycles in the n-triangular graph.

0, 0, 16, 920, 7800, 36260, 122080, 334656, 794640, 1696200, 3334320, 6137560, 10706696, 17859660, 28683200, 44591680, 67393440, 99365136, 143334480, 202771800, 281890840, 385759220, 520418976, 693017600, 911950000, 1187011800, 1529564400, 1952712216, 2471492520

Offset: 2

Author

Eric W. Weisstein, Aug 14 2017

Keywords

• nonn
• easy

Links

• Eric Weisstein's World of Mathematics, Graph Cycle
• Eric Weisstein's World of Mathematics, Johnson Graph
• Eric Weisstein's World of Mathematics, Triangular Graph
• Index entries for linear recurrences with constant coefficients, signature (8, -28, 56, -70, 56, -28, 8, -1).

Crossrefs

Cf. A002417 (3-cycles), A151974 (4-cycles), A290939 (5-cycles).

Programs

Mathematica

Table[2 Binomial[n, 4] (n^3 + 27 n^2 - 220 n + 392), {n, 2, 20}]
LinearRecurrence[{8, -28, 56, -70, 56, -28, 8, -1}, {0, 0, 16, 920, 7800, 36260, 122080, 334656}, 20]
CoefficientList[Series[-((4 (-4 x^2 - 198 x^3 - 222 x^4 + 319 x^5))/(-1 + x)^8), {x, 0, 20}], x]

Formula

a(n) = 2*binomial(n, 4) (n^3 + 27*n^2 - 220*n + 392).

a(n) = 8*a(n-1) - 28*a(n-2) + 56*a(n-3) - 70*a(n-4) + 56*a(n-5) - 28*a(n-6) + 8*a(n-7) - a(n-8).

G.f.: -((4*x^2 (-4*x^2 - 198*x^3 - 222*x^4 + 319*x^5))/(-1 + x)^8).