A256914 Trace of the enhanced squares representation of n.
0, 1, 2, 3, 4, 1, 2, 3, 1, 9, 1, 2, 3, 4, 1, 2, 16, 1, 2, 3, 4, 1, 2, 3, 1, 25, 1, 2, 3, 4, 1, 2, 3, 1, 9, 1, 36, 1, 2, 3, 4, 1, 2, 3, 1, 9, 1, 2, 3, 49, 1, 2, 3, 4, 1, 2, 3, 1, 9, 1, 2, 3, 4, 1, 64, 1, 2, 3, 4, 1, 2, 3, 1, 9, 1, 2, 3, 4, 1, 2, 16, 81, 1, 2
Offset: 0
Examples
R(0) = 0, so trace = 0. R(1) = 1, so trace = 1. R(8) = 4 + 3 + 1, so trace = 1. R(43) = 36 + 4 + 3, so trace = 3.
Links
- Clark Kimberling, Table of n, a(n) for n = 0..1000
Programs
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Haskell
a256914 = last . a256913_row -- Reinhard Zumkeller, Apr 15 2015
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Mathematica
b[n_] := n^2; bb = Insert[Table[b[n], {n, 0, 100}] , 2, 3]; s[n_] := Table[b[n], {k, 1, 2 n + 1}]; h[1] = {0, 1, 2, 3}; h[n_] := Join[h[n - 1], s[n]]; g = h[100]; Take[g, 100] r[0] = {0}; r[1] = {1}; r[2] = {2}; r[3] = {3}; r[8] = {4, 3, 1}; r[n_] := If[MemberQ[bb, n], {n}, Join[{g[[n]]}, r[n - g[[n]]]]]; t = Table[r[n], {n, 0, 120}] (* A256913, before concatenation *) Flatten[t] (* A256913 *) Table[Last[r[n]], {n, 0, 120}] (* A256914 *) Table[Length[r[n]], {n, 0, 200}] (* A256915 *)
Comments