OFFSET
1,3
LINKS
Eric Weisstein's World of Mathematics, Complete Bipartite Graph
Eric Weisstein's World of Mathematics, Graph Crossing Number
Index entries for linear recurrences with constant coefficients, signature (2,0,-2,1).
FORMULA
a(n) = 6*floor(n/2)*floor((n-1)/2).
G.f.: -6*x^3/((-1 + x)^3*(1 + x)).
a(n) = 2*a(n-1) - 2*a(n-3) + a(n-4).
a(n) = (3/4)*(2*n*(n - 2) + 1 - (-1)^n).
a(n) = 6*A002620(n-1). - R. J. Mathar, Feb 12 2021
MATHEMATICA
Table[6 Floor[n/2] Floor[(n - 1)/2], {n, 60}]
Table[3/4 (2 n (n - 2) + 1 - (-1)^n), {n, 60}]
LinearRecurrence[{2, 0, -2, 1}, {0, 0, 6, 12}, 60]
CoefficientList[Series[-6 x^2/((-1 + x)^3 (1 + x)), {x, 0, 60}], x]
PROG
(PARI) a(n)=n--^2\4*6 \\ Charles R Greathouse IV, Jul 13 2021
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Eric W. Weisstein, Sep 11 2018
STATUS
approved