A256797 Nonpositive part of the minimal alternating squares representation of n.
0, 2, 1, 0, 4, 4, 4, 1, 0, 10, 9, 4, 4, 4, 1, 0, 9, 11, 10, 9, 4, 4, 4, 1, 0, 20, 9, 9, 11, 10, 9, 4, 4, 4, 1, 0, 16, 20, 20, 9, 9, 11, 10, 9, 4, 4, 4, 1, 0, 18, 17, 16, 20, 20, 9, 9, 11, 10, 9, 4, 4, 4, 1, 0, 16, 16, 18, 17, 16, 20, 20, 9, 9, 11, 10, 9, 4
Offset: 1
Examples
R(1) = 1, positive part 1, nonpositive part 0; R(2) = 4 - 2, positive part 4, nonpositive part 2; R(3) = 4 - 1, positive part 4, nonpositive part 1; R(89) = 100 - 16 + 9 - 4, positive part 100 + 9 = 109, nonpositive part 16 + 4 = 20.
Links
- Clark Kimberling, Table of n, a(n) for n = 1..1000
Programs
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Mathematica
b[n_] := n^2; bb = Table[b[n], {n, 0, 100}]; s[n_] := Table[b[n], {k, 1, 2 n - 1}]; h[1] = {1}; h[n_] := Join[h[n - 1], s[n]]; g = h[100]; r[0] = {0}; r[1] = {1}; r[2] = {4, -2}; r[n_] := If[MemberQ[bb, n], {n}, Join[{g[[n]]}, -r[g[[n]] - n]]]; t = Table[r[n], {n, 1, z}] (* A256789 *) Table[Total[(Abs[r[n]] + r[n])/2], {n, 1, 120}] (* A256796 *) Table[Total[(Abs[r[n]] - r[n])/2], {n, 1, 120}] (* A256797 *)
Comments