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.
From Elmo R. Oliveira, Sep 13 2025: (Start)
E.g.f.: exp(x)*x^3*(x + 3)/3.
a(n) = 2*A004320(n-2) for n >= 2. (End)
From Amiram Eldar, Sep 29 2025: (Start)
Sum_{n>=3} 1/a(n) = (Pi^2-9)/4.
Sum_{n>=3} (-1)^(n+1)/a(n) = Pi^2/8 + 6*log(2) - 21/4. (End)
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