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A256759
Nonpositive part of the minimal alternating triangular-number representation of n (defined at A255974).
2
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
1,4
LINKS
FORMULA
A256700(n) - A256759(n) = n.
EXAMPLE
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
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 *)
CROSSREFS
Sequence in context: A099546 A036870 A036874 * A336090 A255123 A244483
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, Apr 13 2015
STATUS
approved