A256759 - OEIS

%I #4 Apr 13 2015 09:40:40

%S 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,

%T 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,

%U 1,0,18,10,10,11,10,6,6,7,3,3,1,0,15,18

%N Nonpositive part of the minimal alternating triangular-number representation of n (defined at A255974).

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

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

%e R(1) = 1; positive part 1, nonpositive part 0

%e R(2) = 3 - 1; positive part 3, nonpositive part 1

%e R(3) = 3; positive part 3, nonpositive part 0

%e R(11) = 15 - 6 + 3 - 1; positive part 15+3 = 18; nonpositive part 6 + 1 = 7

%t b[n_] := n (n + 1)/2; bb = Table[b[n], {n, 0, 1000}];

%t s[n_] := Table[b[n], {k, 1, n}];

%t h[1] = {1}; h[n_] := Join[h[n - 1], s[n]]; g = h[100]; r[0] = {0};

%t r[n_] := If[MemberQ[bb, n], {n}, Join[{g[[n]]}, -r[g[[n]] - n]]];

%t Table[Total[(Abs[r[n]] + r[n])/2], {n, 1, 120}]  (* A256700 *)

%t Table[Total[(Abs[r[n]] - r[n])/2], {n, 1, 120}]  (* A256759 *)

%Y Cf. A255974, A256701.

%K nonn,easy

%O 1,4

%A _Clark Kimberling_, Apr 13 2015