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A256797
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Nonpositive part of the minimal alternating squares representation of n.
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2
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0, 2, 1, 0, 4, 4, 4, 1, 0, 10, 9, 4, 4, 4, 1, 0, 9, 11, 10, 9, 4, 4, 4, 1, 0, 20, 9, 9, 11, 10, 9, 4, 4, 4, 1, 0, 16, 20, 20, 9, 9, 11, 10, 9, 4, 4, 4, 1, 0, 18, 17, 16, 20, 20, 9, 9, 11, 10, 9, 4, 4, 4, 1, 0, 16, 16, 18, 17, 16, 20, 20, 9, 9, 11, 10, 9, 4
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OFFSET
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1,2
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COMMENTS
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LINKS
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EXAMPLE
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R(1) = 1, positive part 1, nonpositive part 0;
R(2) = 4 - 2, positive part 4, nonpositive part 2;
R(3) = 4 - 1, positive part 4, nonpositive part 1;
R(89) = 100 - 16 + 9 - 4, positive part 100 + 9 = 109, nonpositive part 16 + 4 = 20.
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MATHEMATICA
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b[n_] := n^2; bb = Table[b[n], {n, 0, 100}];
s[n_] := Table[b[n], {k, 1, 2 n - 1}];
h[1] = {1}; h[n_] := Join[h[n - 1], s[n]];
g = h[100]; r[0] = {0}; r[1] = {1}; r[2] = {4, -2};
r[n_] := If[MemberQ[bb, n], {n}, Join[{g[[n]]}, -r[g[[n]] - n]]];
t = Table[r[n], {n, 1, z}] (* A256789 *)
Table[Total[(Abs[r[n]] + r[n])/2], {n, 1, 120}] (* A256796 *)
Table[Total[(Abs[r[n]] - r[n])/2], {n, 1, 120}] (* A256797 *)
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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