A182186 Number b(n) of basic ideals in the Borel subalgebra of the untwisted affine Lie algebra of type B.
24, 128, 648, 3160, 14984, 69536, 317264, 1427912, 6355080, 28021504, 122586224, 532681648, 2301267408, 9891512000, 42327269792, 180410129576, 766250022536, 3244192404032, 13696322822960, 57673821115088, 242287778611184, 1015664308220864, 4249246138360928
Offset: 2
Links
- J. Nilsson, Enumeration of basic ideals in type B
- J. Nilsson, Enumeration of Basic Ideals in Type B Lie Algebras, J. Int. Seq. 15 (2012) #12.9.5
Programs
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Maple
B:=n->(3*n+5)*2^(2*n-2)-(2*(3*n-1))*binomial(2*n-2, n-1): seq(B(n), n=2..30);
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PARI
a(n) = (3*n+5)*2^(2*n-2)-(2*(3*n-1))*binomial(2*n-2, n-1); \\ Michel Marcus, Aug 18 2013
Formula
a(n) = (3*n+5)*2^(2*n-2)-(2*(3*n-1))*binomial(2*n-2, n-1).
a(n) - 8*a(n-1) + 16*a(n-2) = (24/(n-1))*binomial(2*n-6,n-2) for n>3.
-(n-1)*(9*n^2-51*n+76)*a(n) +2*(36*n^3-231*n^2+478*n-295)*a(n-1) -8*(2*n-5)*(9*n^2-33*n+34)*a(n-2)=0. - R. J. Mathar, Oct 27 2017
Comments