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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, 57673821115088, 242287778611184, 1015664308220864, 4249246138360928 (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 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 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 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); PROG (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 CROSSREFS Cf. A000984, A194460. Sequence in context: A044737 A305159 A326367 * A188304 A167981 A185490 Adjacent sequences:  A182183 A182184 A182185 * A182187 A182188 A182189 KEYWORD nonn,easy AUTHOR Jonathan Nilsson, Apr 16 2012 STATUS approved

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Last modified March 29 15:16 EDT 2020. Contains 333107 sequences. (Running on oeis4.)