OFFSET
1,2
COMMENTS
The only chordless cycles in a complete tripartite graph are cycles of length 4 confined to two of the partitions. - Andrew Howroyd, Jan 03 2018
LINKS
Eric Weisstein's World of Mathematics, Chordless Cycle
Eric Weisstein's World of Mathematics, Complete Tripartite Graph
Index entries for linear recurrences with constant coefficients, signature (5, -10, 10, -5, 1).
FORMULA
a(n) = 3*n^2*(n-1)^2/4 = 3*A000537(n). - Andrew Howroyd, Jan 03 2018
a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5).
G.f.: -3*x^2*(1 + 4*x + x^2)/(-1 + x)^5.
MATHEMATICA
Table[3 Binomial[n, 2]^2, {n, 20}]
3 Binomial[Range[20], 2]^2
LinearRecurrence[{5, -10, 10, -5, 1}, {0, 3, 27, 108, 300}, 20]
SeriesCoefficient[Series[-3 x (1 + 4 x + x^2)/(-1 + x)^5, {x, 0, 20}], x]
PROG
(PARI) a(n) = 3*n^2*(n-1)^2/4; \\ Andrew Howroyd, Jan 03 2018
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Eric W. Weisstein, Jan 02 2018
EXTENSIONS
a(6)-a(36) from Andrew Howroyd, Jan 03 2018
STATUS
approved