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A182186 Number b(n) of basic ideals in the Borel subalgebra of the untwisted affine Lie algebra of type B. 0
24, 128, 648, 3160, 14984, 69536, 317264, 1427912, 6355080, 28021504, 122586224, 532681648, 2301267408, 9891512000, 42327269792, 180410129576, 766250022536, 3244192404032, 13696322822960 (list; graph; refs; listen; history; text; internal format)
OFFSET

2,1

COMMENTS

The corresponding sequence for the usual type B Lie algebra is given by the central binomial coefficients A000984.

LINKS

Table of n, a(n) for n=2..20.

J. Nilsson: Enumeration of basic ideals in type B

FORMULA

b(n) = (3*n+5)*2^(2*n-2)-(2*(3*n-1))*binomial(2*n-2, n-1).

b(n) - 8*b(n-1) + 16*b(n-2) = (24/(n-1))*binomial(2*n-6,n-2) for n>3.

MAPLE

B:=n->(3*n+5)*2^(2*n-2)-(2*(3*n-1))*binomial(2*n-2, n-1);

CROSSREFS

Cf. A000984, A194460.

Sequence in context: A042120 A044356 A044737 * A188304 A167981 A185490

Adjacent sequences:  A182183 A182184 A182185 * A182187 A182188 A182189

KEYWORD

nonn

AUTHOR

Jonathan Nilsson, Apr 16 2012

STATUS

approved

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Last modified June 18 22:35 EDT 2013. Contains 226356 sequences.