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A336725
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A(n,k) is the n-th number that is a sum of k positive k-th powers; square array A(n,k), n>=1, k>=1, read by antidiagonals.
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10
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1, 2, 2, 3, 5, 3, 4, 10, 8, 4, 5, 19, 17, 10, 5, 6, 36, 34, 24, 13, 6, 7, 69, 67, 49, 29, 17, 7, 8, 134, 132, 98, 64, 36, 18, 8, 9, 263, 261, 195, 129, 84, 43, 20, 9, 10, 520, 518, 388, 258, 160, 99, 55, 25, 10, 11, 1033, 1031, 773, 515, 321, 247, 114, 62, 26, 11, 12, 2058, 2056, 1542, 1028, 642, 384, 278, 129, 66, 29, 12
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OFFSET
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1,2
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LINKS
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EXAMPLE
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Square array A(n,k) begins:
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, ...
2, 5, 10, 19, 36, 69, 134, 263, 520, 1033, ...
3, 8, 17, 34, 67, 132, 261, 518, 1031, 2056, ...
4, 10, 24, 49, 98, 195, 388, 773, 1542, 3079, ...
5, 13, 29, 64, 129, 258, 515, 1028, 2053, 4102, ...
6, 17, 36, 84, 160, 321, 642, 1283, 2564, 5125, ...
7, 18, 43, 99, 247, 384, 769, 1538, 3075, 6148, ...
8, 20, 55, 114, 278, 734, 896, 1793, 3586, 7171, ...
9, 25, 62, 129, 309, 797, 2193, 2048, 4097, 8194, ...
10, 26, 66, 164, 340, 860, 2320, 6568, 4608, 9217, ...
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MAPLE
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A:= proc() local l, w, A; l, w, A:= proc() [] end, proc() [] end,
proc(n, k) option remember; local b; b:=
proc(x, y) option remember; `if`(x=0, {0}, `if`(y<1, {},
{b(x, y-1)[], map(t-> t+l(k)[y], b(x-1, y))[]}))
end;
while nops(w(k)) < n do forget(b);
l(k):= [l(k)[], (nops(l(k))+1)^k];
w(k):= sort([select(h-> h<l(k)[-1], b(k, nops(l(k))))[]])
od; w(k)[n]
end; A
end():
seq(seq(A(n, 1+d-n), n=1..d), d=1..12);
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MATHEMATICA
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nmax = 12;
pow[n_, k_] := IntegerPartitions[n, {k}, Range[n^(1/k) // Ceiling]^k];
col[k_] := col[k] = Reap[Module[{j = k, n = 1, p}, While[n <= nmax, p = pow[j, k]; If[p =!= {}, Sow[j]; n++]; j++]]][[2, 1]];
A[n_, k_] := col[k][[n]];
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CROSSREFS
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Columns k=1-11 give: A000027, A000404, A003072, A003338, A003350, A003362, A003374, A003386, A003398, A004810, A004822.
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KEYWORD
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AUTHOR
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STATUS
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approved
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