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A140985
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First row of infinite array A(j,k): A(j,1) = j-1; A(1,k) = A(2,k-1); for j, k > 1, A(j,k) = A(j-1,k) - A(j+1,k-1) if that number is positive and not already in column k, A(j,k) = A(j-1,k) + A(j+1,k-1) otherwise.
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1
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0, 1, 3, 9, 2, 18, 15, 69, 228, 90, 58, 438, 174, 1540, 579, 4957, 1860, 6340, 3572, 20646, 10276, 72070, 33978, 21794, 134644, 66308, 32884, 284546, 154006, 12326, 132691, 609297, 281174, 1777074, 813864, 485328, 3663226, 1659946, 5081036
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OFFSET
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1,3
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COMMENTS
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The natural numbers preceded by 0 constitute the first column; the other columns are built by a slight modification of the definition of Recamán's sequence. E.g., the second column is Recamán's sequence deprived of its first term 0 (cf. A005132).
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LINKS
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EXAMPLE
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Upper left triangle of the array is
0 1 3 9 2 18 15 69 228...
1 3 9 2 18 15 69 228...
2 6 7 16 3 54 159 ...
3 2 14 15 39 90 ...
4 7 1 36 36 ...
5 13 21 3 ...
6 20 33 ...
7 12 ...
8 ...
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PROG
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(PARI) {m=40; A=matrix(m, m); k=1; for(j=1, m, A[j, k]=j-1); print1(A[1, k], ", "); for(k=2, m, print1(A[1, k]=A[2, k-1], ", "); s=Set(A[1, k]); for(j=2, m-k+1, e=A[j-1, k]-A[j+1, k-1]; if((e>0)&&!setsearch(s, e), A[j, k]=e, A[j, k]=A[j-1, k]+A[j+1, k-1]); s=setunion(s, Set(A[j, k]))))} \\ Klaus Brockhaus, Aug 05 2008
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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Philippe Lallouet (philip.lallouet(AT)orange.fr), Jul 28 2008
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EXTENSIONS
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STATUS
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approved
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