OFFSET
0,3
COMMENTS
a(n) is the number of edges of the shuffle-exchange graph SE_n with self-loops removed.
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..1000
D. Kleitman, F. T. Leighton, M. Lepley, and G. L. Miller, New layouts for the shuffle-exchange graph (Extended Abstract), Proceedings of the 13th annual ACM symposium on Theory of Computing (STOC '81), 1981, 278-292.
Eric Weisstein's World of Mathematics, Shuffle-Exchange Graph
Index entries for linear recurrences with constant coefficients, signature (2,1,-2).
FORMULA
G.f.: x*(3*x^2+x+1)/((x-1)*(2*x-1)*(x+1)).
a(n) = 3*2^(n-1) -3 + (n mod 2) for n>0, a(0) = 0.
MAPLE
a:= n-> `if`(n=0, 0, 3*2^(n-1) -3 +irem(n, 2)):
seq(a(n), n=0..40);
MATHEMATICA
LinearRecurrence[{2, 1, -2}, {0, 1, 3, 10}, 40] (* Harvey P. Dale, Mar 23 2018 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Alois P. Heinz, May 06 2012
STATUS
approved