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A042971
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a(n) = (C(2n, n)/2 - (2^(n-1) + ((n+1) mod 2)*C(n-1, n/2-1)))/2.
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2
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0, 0, 3, 12, 55, 210, 826, 3136, 12027, 45870, 175846, 674784, 2598102, 10024196, 38771188, 150250496, 583368787, 2268706134, 8836184878, 34461323872, 134563944322, 526023515996, 2058355584748, 8061896050432, 31602643220830, 123979613859660, 486734822857596
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OFFSET
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1,3
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COMMENTS
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Number of distinct asymmetric staircase walks connecting opposite corners of a square grid of side n > 1. - Christian Barrientos, Nov 25 2018
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LINKS
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EXAMPLE
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U = up, R = right Example of asymmetric staircase walk: URURUURR. - Christian Barrientos, Nov 29 2018
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MATHEMATICA
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Table[Binomial[2n, n]/2-(2^(n-1)+Mod[n+1, 2]Binomial[n-1, n/2-1]), {n, 30}]/2
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PROG
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(PARI) a(n) = (binomial(2*n, n)/2 - (2^(n-1) + if (((n+1) % 2), binomial( n-1, n/2-1))))/2; \\ Michel Marcus, Nov 25 2018
(Magma) [(Binomial(2*n, n) -(2^n +(1+(-1)^n)*Binomial(n-1, Floor(n/2)-1) ))/4: n in [1..30]]; // G. C. Greubel, Feb 17 2019
(Sage) [(binomial(2*n, n) -(2^n + (1+(-1)^n)*binomial(n-1, floor(n/2)-1)))/4 for n in (1..30)] # G. C. Greubel, Feb 17 2019
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CROSSREFS
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Cf. A027306 (for symmetric staircase walks).
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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