OFFSET
1,1
LINKS
Eric Weisstein's World of Mathematics, Complete Bipartite Graph.
Eric Weisstein's World of Mathematics, Molecular Topological Index.
Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).
FORMULA
a(n) = 4*n^2*(2*n-1).
a(n) = 4*A015237(n).
G.f.: 4*x*(3*x^2+8*x+1)/(x-1)^4. - Colin Barker, Nov 04 2012
a(n) = 2*n * A002939(n). - Bruce J. Nicholson, Oct 14 2019
E.g.f.: 4*exp(x)*x*(1 + 5*x + 2*x^2). - Stefano Spezia, Oct 15 2019
From Amiram Eldar, Dec 11 2025: (Start)
Sum_{n>=1} 1/a(n) = log(2) - Pi^2/24.
Sum_{n>=1} (-1)^(n+1)/a(n) = Pi/4 - Pi^2/48 - log(2)/2. (End)
MATHEMATICA
Table[4n^2(2n-1), {n, 30}] (* or *) LinearRecurrence[{4, -6, 4, -1}, {4, 48, 180, 448}, 30] (* Harvey P. Dale, Apr 08 2018 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Eric W. Weisstein, Jul 10 2011
EXTENSIONS
More terms from Amiram Eldar, Dec 11 2025
STATUS
approved