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A190360
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Number of one-sided n-step prudent walks, avoiding 4 or more consecutive east steps.
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2
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1, 3, 7, 17, 40, 96, 229, 547, 1306, 3119, 7448, 17786, 42473, 101426, 242206, 578390, 1381200, 3298317, 7876408, 18808927, 44915872, 107259471, 256136497, 611656057, 1460639684, 3488019553, 8329419319, 19890721694, 47499206650
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OFFSET
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0,2
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COMMENTS
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a(n,k) is the number of one-sided n-step prudent walks, avoiding k or more consecutive east steps; k=4 in this sequence.
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LINKS
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FORMULA
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G.f.: (1+t-t^k)/(1-2*t-t^2+t^(k+1)), (k=4 in this sequence).
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MAPLE
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b:= proc(n, i) option remember; `if`(n<0, 0,
`if`(n=0, 1, b(n-1, 0) +`if`(i<=0, b(n-1, -1), 0)+
`if`(i>=0 and i<3, b(n-1, i+1), 0)))
end:
a:= n-> b(n, 0):
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MATHEMATICA
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(1+t-t^k)/(1-2*t-t^2+t^(k+1)) /. k -> 4 + O[t]^25 // CoefficientList[#, t]& (* Jean-François Alcover, Oct 24 2016 *)
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CROSSREFS
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KEYWORD
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nonn,walk,changed
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AUTHOR
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STATUS
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approved
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