login
A290940
Number of 6-cycles in the n-triangular graph.
3
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
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
KEYWORD
nonn,easy
AUTHOR
Eric W. Weisstein, Aug 14 2017
STATUS
approved