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A059219
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Variation of Boustrophedon transform applied to sequence 1,0,0,0,...: fill an array by diagonals in alternating directions - 'up' and 'down'. The first element of each diagonal after the first is 0. When 'going up', add to the previous element the elements of the row the new element is in. When 'going down', add to the previous element the elements of the column the new element is in. The final element of the n-th diagonal is a(n).
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20
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1, 1, 2, 5, 15, 55, 239, 1199, 6810, 43108, 300731, 2291162, 18923688, 168402163, 1606199354, 16345042652, 176758631046, 2024225038882, 24471719797265, 311446235344127, 4162172487402027, 58275220793611957, 853045299274146032
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OFFSET
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0,3
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LINKS
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EXAMPLE
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The array begins
1 1 0 5 0 55 0 ...
0 1 3 5 48 55 ...
2 2 8 39 103 ...
0 12 27 152 ...
15 15 190 ...
0 221 ...
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MAPLE
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aaa := proc(m, n) option remember; local j, s, t1; if m=0 and n=0 then RETURN(1); fi; if n = 0 and m mod 2 = 1 then RETURN(0); fi; if m = 0 and n mod 2 = 0 then RETURN(0); fi; s := m+n; if s mod 2 = 1 then t1 := aaa(m+1, n-1); for j from 0 to n-1 do t1 := t1+aaa(m, j); od: else t1 := aaa(m-1, n+1); for j from 0 to m-1 do t1 := t1+aaa(j, n); od: fi; RETURN(t1); end; # the n-th antidiagonal in the up direction is aaa(n, 0), aaa(n-1, 1), aaa(n-2, 2), ..., aaa(0, n)
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MATHEMATICA
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max = 22; t[0, 0] = 1; t[0, _?EvenQ] = 0; t[_?OddQ, 0] = 0; t[n_, k_] /; OddQ[n+k](* up *):= t[n, k] = t[n+1, k-1] + Sum[t[n, j], {j, 0, k-1}]; t[n_, k_] /; EvenQ[n+k](* down *):= t[n, k] = t[n-1, k+1] + Sum[t[j, k], {j, 0, n-1}]; tnk = Table[t[n, k], {n, 0, max}, {k, 0, max-n}]; Join[{1}, Rest[Union[tnk[[1]], tnk[[All, 1]]]]](* Jean-François Alcover, May 16 2012 *)
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CROSSREFS
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KEYWORD
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easy,nonn,nice
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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