A290939 Number of 5-cycles in the n-triangular graph.

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

Table of n, a(n) for n=2..33.

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 (7,-21,35,-35,21,-7,1).

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

Adjacent sequences: A290936 A290937 A290938 * A290940 A290941 A290942

Keyword

nonn,easy

Author

Eric W. Weisstein, Aug 14 2017

Status

approved