OFFSET
1,3
LINKS
Andrew Howroyd, Table of n, a(n) for n = 1..1000
Eric Weisstein's World of Mathematics, Graph Cycle
Eric Weisstein's World of Mathematics, Rook Graph
Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1).
FORMULA
a(n) = 2*n*binomial(n,3).
a(n) = 5*a(n-1)-10*a(n-2)+10*a(n-3)-5*a(n-4)+a(n-5).
G.f.: (-2*x^3*(3+x))/(-1+x)^5.
MATHEMATICA
Table[n^2 (n - 1) (n - 2)/3, {n, 20}]
Table[2 n Binomial[n, 3], {n, 20}]
LinearRecurrence[{5, -10, 10, -5, 1}, {0, 0, 6, 32, 100}, 20]
CoefficientList[Series[-((2 x^2 (3 + x))/(-1 + x)^5), {x, 0, 20}], x]
PROG
(PARI) a(n) = {2*n*binomial(n, 3)} \\ Andrew Howroyd, Apr 26 2020
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Eric W. Weisstein, Jun 20 2017
EXTENSIONS
Terms a(31) and beyond from Andrew Howroyd, Apr 26 2020
STATUS
approved