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A256914
Trace of the enhanced squares representation of n.
6
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
0,3
COMMENTS
See A256913 for definitions.
a(A257046(n)) = 1; a(A257047(n)) != 1. - Reinhard Zumkeller, Apr 15 2015
LINKS
EXAMPLE
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.
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 *)
PROG
(Haskell)
a256914 = last . a256913_row -- Reinhard Zumkeller, Apr 15 2015
CROSSREFS
Cf. A000290, A256913, A256915 (number of terms).
Sequence in context: A078978 A322424 A309198 * A171171 A159957 A053840
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, Apr 14 2015
STATUS
approved