|
| |
|
|
A032123
|
|
Number of 2n-bead black-white reversible strings with n black beads.
|
|
1
|
|
|
|
1, 1, 4, 10, 38, 126, 472, 1716, 6470, 24310, 92504, 352716, 1352540, 5200300, 20060016, 77558760, 300546630, 1166803110, 4537591960, 17672631900, 68923356788, 269128937220, 1052049834576, 4116715363800
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
0,3
|
|
|
COMMENTS
|
It appears that a(n) is also the number of quivers in the mutation class of affine B_n or affine type C_n for n>=2. [From Christian Stump, Nov 02 2010]
|
|
|
LINKS
|
Table of n, a(n) for n=0..23.
C. G. Bower, Transforms (2)
N. J. A. Sloane, Classic Sequences
|
|
|
FORMULA
|
n odd: C(2n-1, n-1); n even: C(2n-1, n-1) + C(n-1, n/2-1)
"BIK[ n ](2n-1)" (reversible, indistinct, unlabeled, n parts, 2n-1 elements) transform of 1, 1, 1, 1...
E.g.f.: exp(x)*cosh(x)*BesselI(0, 2*x). - Vladeta Jovovic, Apr 07 2005
G.f.: (1/2)*((1-4*x)^(-1/2)+(1-4*x^2)^(-1/2)) - Mark van Hoeij, Oct 30 2011.
|
|
|
CROSSREFS
|
Central column of Losanitsch's triangle A034851.
Sequence in context: A197051 A149191 A149192 * A149193 A149194 A149195
Adjacent sequences: A032120 A032121 A032122 * A032124 A032125 A032126
|
|
|
KEYWORD
|
nonn,changed
|
|
|
AUTHOR
|
Christian G. Bower
|
|
|
STATUS
|
approved
|
| |
|
|
