A256911 Number of terms in the enhanced triangular-number representation of n.

1, 1, 1, 1, 2, 2, 1, 2, 2, 2, 1, 2, 2, 2, 3, 1, 2, 2, 2, 3, 3, 1, 2, 2, 2, 3, 3, 2, 1, 2, 2, 2, 3, 3, 2, 3, 1, 2, 2, 2, 3, 3, 2, 3, 3, 1, 2, 2, 2, 3, 3, 2, 3, 3, 3, 1, 2, 2, 2, 3, 3, 2, 3, 3, 3, 2, 1, 2, 2, 2, 3, 3, 2, 3, 3, 3, 2, 3, 1, 2, 2, 2, 3, 3, 2, 3

Offset

0,5

Comments

See A256909 for definitions. The least n for which R(n) has 5 terms is given by R(7259) = 7140 + 105 + 10 + 3 + 1.

Links

Clark Kimberling, Table of n, a(n) for n = 0..1000

Example

R(4) = 3 + 1, so a(4) = 2.
R(119) = 105 + 10 + 3 + 1, so a(119) = 4.

Mathematica

b[n_] := n (n + 1)/2; bb = Insert[Table[b[n], {n, 0, 200}], 2, 3]
s[n_] := Table[b[n], {k, 1, n + 1}];
h[1] = {0, 1, 2}; h[n_] := Join[h[n - 1], s[n]];
g = h[200]; r[0] = {0};
r[n_] := If[MemberQ[bb, n], {n}, Join[{g[[n]]}, r[n - g[[n]]]]];
t = Table[r[n], {n, 0, 120}] (*A256909 before concatenation*)
Flatten[t]  (*A256909*)
Table[Last[r[n]], {n, 0, 120}]    (*A256910*)
Table[Length[r[n]], {n, 0, 120}]  (*A256911*)

Crossrefs

Cf. A000217, A256909 (representations) A256910 (trace).

Sequence in context: A169818 A367816 A116543 * A347562 A359790 A107260

Adjacent sequences: A256908 A256909 A256910 * A256912 A256913 A256914

Keyword

nonn,easy

Author

Clark Kimberling, Apr 14 2015

Status

approved