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A192033 Expansion of x*(3*x^2+x+1)/((x-1)*(2*x-1)*(x+1)). 2
0, 1, 3, 10, 21, 46, 93, 190, 381, 766, 1533, 3070, 6141, 12286, 24573, 49150, 98301, 196606, 393213, 786430, 1572861, 3145726, 6291453, 12582910, 25165821, 50331646, 100663293, 201326590, 402653181, 805306366, 1610612733, 3221225470, 6442450941, 12884901886 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,3
COMMENTS
a(n) is the number of edges of the shuffle-exchange graph SE_n with self-loops removed.
LINKS
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
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
Cf. A240802.
Sequence in context: A007687 A330273 A335666 * A295063 A298856 A006308
KEYWORD
nonn,easy
AUTHOR
Alois P. Heinz, May 06 2012
STATUS
approved

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Last modified March 29 02:22 EDT 2024. Contains 371264 sequences. (Running on oeis4.)