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A256700
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Positive part of the minimal alternating triangular-number representation of n (defined at A255974).
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2
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1, 3, 3, 7, 6, 6, 10, 11, 10, 10, 18, 15, 16, 15, 15, 22, 24, 21, 22, 21, 21, 28, 29, 31, 28, 29, 28, 28, 39, 36, 37, 39, 36, 37, 36, 36, 48, 48, 45, 46, 48, 45, 46, 45, 45, 56, 58, 58, 55, 56, 58, 55, 56, 55, 55, 66, 67, 69, 69, 66, 67, 69, 66, 67, 66, 66
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OFFSET
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1,2
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LINKS
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FORMULA
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EXAMPLE
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R(1) = 1; positive part 1, nonpositive part 0
R(2) = 3 - 1; positive part 3, nonpositive part 1
R(3) = 3; positive part 3, nonpositive part 0
R(11) = 15 - 6 + 3 - 1; positive part 15+3 = 18; nonpositive part 6 + 1 = 7
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MATHEMATICA
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b[n_] := n (n + 1)/2; bb = Table[b[n], {n, 0, 1000}];
s[n_] := Table[b[n], {k, 1, n}];
h[1] = {1}; h[n_] := Join[h[n - 1], s[n]]; g = h[100]; r[0] = {0};
r[n_] := If[MemberQ[bb, n], {n}, Join[{g[[n]]}, -r[g[[n]] - n]]];
Table[Total[(Abs[r[n]] + r[n])/2], {n, 1, 120}] (* A256700 *)
Table[Total[(Abs[r[n]] - r[n])/2], {n, 1, 120}] (* A256759 *)
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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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