proposed

approved

editing

proposed

allocated for Clark KimberlingNonpositive 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

1,4

Clark Kimberling, <a href="/A256759/b256759.txt">Table of n, a(n) for n = 1..1000</a>

A256700(n) - A256759(n) = n.

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

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 *)

Cf. A255974, A256701.

allocated

nonn,easy

Clark Kimberling, Apr 13 2015

approved

editing

allocated for Clark Kimberling

allocated

approved