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

2,3

Links

Table of n, a(n) for n=2..30.

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).

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).

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]

Crossrefs

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

Sequence in context: A289707 A006089 A260620 * A173953 A211105 A276637

Adjacent sequences: A290937 A290938 A290939 * A290941 A290942 A290943

Keyword

nonn,easy

Author

Eric W. Weisstein, Aug 14 2017

Status

approved