OFFSET
1,3
LINKS
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 (6, -15, 20, -15, 6, -1).
FORMULA
a(n) = n*binomial(n,2)*(n^2-4*n+5)/2.
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).
G.f.: (x^2*(1+3*x+21*x^2+5*x^3))/(-1+x)^6.
MATHEMATICA
Table[n^2 (n - 1) (n^2 - 4 n + 5)/4, {n, 20}]
Table[n Binomial[n, 2] (n^2 - 4 n + 5)/2, {n, 20}]
LinearRecurrence[{6, -15, 20, -15, 6, -1}, {0, 1, 9, 60, 250, 765}, 20]
CoefficientList[Series[(x (1 + 3 x + 21 x^2 + 5 x^3))/(-1 + x)^6, {x, 0, 20}], x]
PROG
(Magma) [n^2*(n-1)*(n^2-4*n+5)/4 : n in [1..50]]; // Wesley Ivan Hurt, Apr 23 2021
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Eric W. Weisstein, Jun 20 2017
STATUS
approved