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 A214623 Braid numbers B((n,n)->(n,n)). 0
 1, 2, 16, 128, 1156, 10952, 107584, 1083392, 11115556, 115702472, 1218289216, 12948910592, 138708574096, 1495661223968, 16218468710656, 176727219273728, 1933956651447076, 21243204576601928, 234121111199439424, 2587943032046002688 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS The number of different possible outcomes when starting with two piles of n distinct playing cards and repeatedly moving a top card from either of these two piles to one of two new piles, until both new piles have height n. For even values of n, a(n) is a square, while for odd values of n, a(n) is twice a square. LINKS J. de Ruiter, Counting Classes of Klondike Solitaire Configurations, Master's Thesis (2012), 48-58. FORMULA G.f.: hypergeom([1/12, 5/12],,1728/(16*x^4-32*x^3-24*x^2-8*x+1)^3*x^4*(4*x^2-12*x+1)*(2*x+1)^2)/(16*x^4-32*x^3-24*x^2-8*x+1)^(1/4); (based on guessed recurrence). - Mark van Hoeij, Apr 11 2014 a(n) = (-2)^n*hypergeom([1/2, -n, n + 1], [1, 1], 2). - Peter Luschny, Mar 14 2018 a(n) ~ 2^(n - 3/2) * (1 + sqrt(2))^(2*n + 1) / (Pi*n). - Vaclav Kotesovec, Jun 09 2019 MATHEMATICA a[n_] := (-2)^n HypergeometricPFQ[{1/2, -n, n + 1}, {1, 1}, 2]; Table[a[n], {n, 0, 19}] (* Peter Luschny, Mar 14 2018 *) CROSSREFS Sequence in context: A322297 A013730 A270924 * A333719 A161737 A171451 Adjacent sequences:  A214620 A214621 A214622 * A214624 A214625 A214626 KEYWORD nonn AUTHOR Johan de Ruiter, Jul 23 2012 STATUS approved

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Last modified July 2 09:21 EDT 2020. Contains 335398 sequences. (Running on oeis4.)