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A153361
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Number of zig-zag paths from top to bottom of a rectangle of width 12 with n rows.
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0
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12, 22, 42, 80, 154, 296, 572, 1104, 2138, 4136, 8020, 15536, 30148, 58450, 113472, 220110, 427410, 829352, 1610628, 3125954, 6071028, 11784514, 22887536, 44431506, 86293452, 167532792, 325373382, 631721620, 1226878704, 2382108386
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OFFSET
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1,1
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COMMENTS
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Number of words of length n using a 12-symbol alphabet where neighboring letters are neighbors in the alphabet. - Andrew Howroyd, Apr 17 2017
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LINKS
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FORMULA
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G.f.: -2*x*(3*x^5 + 12*x^4 - 12*x^3 - 20*x^2 + 5*x + 6)/(x^6 + 3*x^5 - 6*x^4 - 4*x^3 + 5*x^2 + x - 1). - Colin Barker, Sep 02 2012
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MATHEMATICA
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b[n_, i_, k_] := b[n, i, k] = If[n == 0, 1, If[i == 0, Sum[b[n - 1, j, k], {j, 1, k}], If[i > 1, b[n - 1, i - 1, k], 0] + If[i < k, b[n - 1, i + 1, k], 0]]]; a[n_] := b[n, 0, 12]; Array[a, 30] (* Jean-François Alcover, Oct 10 2017, after Alois P. Heinz *)
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CROSSREFS
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KEYWORD
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easy,nonn
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AUTHOR
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STATUS
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approved
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