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A054444
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Even-indexed terms of A001629(n), n >= 2, (Fibonacci convolution).
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7
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1, 5, 20, 71, 235, 744, 2285, 6865, 20284, 59155, 170711, 488400, 1387225, 3916061, 10996580, 30737759, 85573315, 237387960, 656451269, 1810142185, 4978643596, 13661617195, 37409025455, 102238082976, 278920277425, 759695287349
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OFFSET
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0,2
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COMMENTS
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8*a(n) is the number of Boolean (equivalently, lattice, modular lattice, distributive lattice) intervals of the form [s,w] in the Bruhat order on S_n, where s is a simple reflection. - Bridget Tenner, Jan 16 2020
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LINKS
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Jinyuan Wang, Table of n, a(n) for n = 0..1000
É. Czabarka, R. Flórez, and L. Junes, A Discrete Convolution on the Generalized Hosoya Triangle, Journal of Integer Sequences, 18 (2015), #15.1.6.
Guo-Niu Han, Enumeration of Standard Puzzles, 2011. [Cached copy]
Guo-Niu Han, Enumeration of Standard Puzzles, arXiv:2006.14070 [math.CO], 2020.
B. E. Tenner, Interval structures in the Bruhat and weak orders, arXiv:2001.05011 [math.CO], 2020.
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FORMULA
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a(n) = ((2*n+1)*F(2*(n+1)) + 4*(n+1)*F(2*n+1))/5, with F(n) = A000045(n) (Fibonacci numbers).
a(n)= A060920(n+1, 1).
G.f.: (1 - x + x^2)/(1 - 3*x + x^2)^2.
a(n) = Sum_{k=1..n+1} k*binomial(2*n-2*k+2, k). - Emeric Deutsch, Jun 11 2003
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PROG
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(PARI) a(n) = ((2*n+1)*fibonacci(2*(n+1))+4*(n+1)*fibonacci(2*n+1))/5; \\ Jinyuan Wang, Jul 28 2019
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CROSSREFS
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Cf. A000045, A001629, A001870, A060920.
Sequence in context: A054889 A056384 A036683 * A121332 A122695 A269914
Adjacent sequences: A054441 A054442 A054443 * A054445 A054446 A054447
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KEYWORD
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easy,nonn
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AUTHOR
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Wolfdieter Lang, Apr 07 2000
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STATUS
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approved
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