A300846 a(n) = 3*(n - 1)^2*n^3.

0, 0, 24, 324, 1728, 6000, 16200, 37044, 75264, 139968, 243000, 399300, 627264, 949104, 1391208, 1984500, 2764800, 3773184, 5056344, 6666948, 8664000, 11113200, 14087304, 17666484, 21938688, 27000000, 32955000, 39917124, 48009024, 57362928, 68121000

Offset

0,3

Comments

Also the number of 5-cycles in the complete tripartite graph K_{n,n,n} for n >= 1.

Links

Table of n, a(n) for n=0..30.

Eric Weisstein's World of Mathematics, Graph Cycle

Eric Weisstein's World of Mathematics, Complete Tripartite Graph

Index entries for linear recurrences with constant coefficients, signature (6,-15,20,-15,6,-1).

Formula

G.f.: 12*x^2*(2 + 15*x + 12*x^2 + x^3)/(x - 1)^6.

a(n) = 6*a(n-1) - 15*a(n-2) + 20*a(n-3) - 15*a(n-4) + 6*a(n-5) - a(n-6).

a(n) = 3*A099762(n-1).

a(n) = 3*(n - 1)^5 + 9*(n - 1)^4 + 9*(n - 1)^3 + 3*(n - 1)^2.

Mathematica

Table[3 (n - 1)^2 n^3, {n, 0, 20}]
LinearRecurrence[{6, -15, 20, -15, 6, -1}, {0, 0, 24, 324, 1728, 6000}, 20]
CoefficientList[Series[12 x^2 (2 + 15 x + 12 x^2 + x^3)/(x - 1)^6, {x, 0, 20}], x]

Prog

(PARI) a(n) = 3*(n-1)^2*n^3; \\ Altug Alkan, Mar 13 2018

Crossrefs

Sequence in context: A199301 A239793 A289706 * A006922 A036221 A022652

Adjacent sequences: A300843 A300844 A300845 * A300847 A300848 A300849

Keyword

nonn,easy

Author

Eric W. Weisstein, Mar 13 2018

Status

approved