A256759 Nonpositive part of the minimal alternating triangular-number representation of n (defined at A255974).
0, 1, 0, 3, 1, 0, 3, 3, 1, 0, 7, 3, 3, 1, 0, 6, 7, 3, 3, 1, 0, 6, 6, 7, 3, 3, 1, 0, 10, 6, 6, 7, 3, 3, 1, 0, 11, 10, 6, 6, 7, 3, 3, 1, 0, 10, 11, 10, 6, 6, 7, 3, 3, 1, 0, 10, 10, 11, 10, 6, 6, 7, 3, 3, 1, 0, 18, 10, 10, 11, 10, 6, 6, 7, 3, 3, 1, 0, 15, 18
Offset: 1
Examples
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
Links
- Clark Kimberling, Table of n, a(n) for n = 1..1000
Programs
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Mathematica
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 *)