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A290939
Number of 5-cycles in the n-triangular graph.
3
0, 0, 24, 312, 1584, 5376, 14448, 33264, 68544, 129888, 230472, 387816, 624624, 969696, 1458912, 2136288, 3055104, 4279104, 5883768, 7957656, 10603824, 13941312, 18106704, 23255760, 29565120, 37234080, 46486440, 57572424, 70770672, 86390304, 104773056, 126295488
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
FORMULA
a(n) = 12/5 * binomial(n, 4) * (n^2 + 7*n - 34).
a(n) = 7*a(n-1) - 21*a(n-2) + 35*a(n-3) - 35*a(n-4) + 21*a(n-5) - 7*a(n-6) + a(n-7).
G.f.: (24 x^2 (-x^2 - 6 x^3 + 4 x^4))/(-1 + x)^7.
MATHEMATICA
Table[12/5 Binomial[n, 4] (n^2 + 7 n - 34), {n, 2, 20}]
LinearRecurrence[{7, -21, 35, -35, 21, -7, 1}, {0, 0, 24, 312, 1584, 5376, 14448}, 20]
CoefficientList[Series[(24 (-x^2 - 6 x^3 + 4 x^4))/(-1 + x)^7, {x, 0, 20}], x]
PROG
(PARI) a(n)=12*binomial(n, 4)*(n^2+7*n-34)/5 \\ Charles R Greathouse IV, Aug 14 2017
CROSSREFS
Cf. A002417 (number of 3-cycles in the triangular graph), A151974 (4-cycles), A290940 (6-cycles).
Sequence in context: A096821 A168303 A053215 * A004413 A319554 A069779
KEYWORD
nonn,easy
AUTHOR
Eric W. Weisstein, Aug 14 2017
STATUS
approved