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A319047
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Square array A(n,k) where column k is balanced (2k+1)-ary enumeration of integers; n>=0, k>=1, read by antidiagonals.
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5
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0, 0, 1, 0, 1, -1, 0, 1, 2, 3, 0, 1, 2, -2, 4, 0, 1, 2, 3, -1, 2, 0, 1, 2, 3, -3, 5, -3, 0, 1, 2, 3, 4, -2, 6, -2, 0, 1, 2, 3, 4, -4, -1, 7, -4, 0, 1, 2, 3, 4, 5, -3, 7, 3, 9, 0, 1, 2, 3, 4, 5, -5, -2, 8, 4, 10, 0, 1, 2, 3, 4, 5, 6, -4, -1, 9, 10, 8, 0, 1, 2, 3, 4, 5, 6, -6, -3, 9, 10, 11, 12
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OFFSET
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0,9
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LINKS
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EXAMPLE
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Square array A(n,k) begins:
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, ...
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, ...
-1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, ...
3, -2, 3, 3, 3, 3, 3, 3, 3, 3, 3, ...
4, -1, -3, 4, 4, 4, 4, 4, 4, 4, 4, ...
2, 5, -2, -4, 5, 5, 5, 5, 5, 5, 5, ...
-3, 6, -1, -3, -5, 6, 6, 6, 6, 6, 6, ...
-2, 7, 7, -2, -4, -6, 7, 7, 7, 7, 7, ...
-4, 3, 8, -1, -3, -5, -7, 8, 8, 8, 8, ...
9, 4, 9, 9, -2, -4, -6, -8, 9, 9, 9, ...
10, 10, 10, 10, -1, -3, -5, -7, -9, 10, 10, ...
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MAPLE
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A:= proc(n, k) option remember; `if`(n=0, 0,
(b-> b*A(iquo(n, b), k)+mods(n, b))(2*k+1))
end:
seq(seq(A(n, 1+d-n), n=0..d), d=0..14);
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MATHEMATICA
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A[n_, k_] := A[n, k] = If[n == 0, 0, With[{b = 2k+1},
b*A[Quotient[n, b], k] + Mod[n, b, -Quotient[b-1, 2]]]];
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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