OFFSET
0,3
COMMENTS
Also the number of 5-cycles in the complete tripartite graph K_{n,n,n} for n >= 1.
LINKS
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
KEYWORD
nonn,easy
AUTHOR
Eric W. Weisstein, Mar 13 2018
STATUS
approved