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A256911
Number of terms in the enhanced triangular-number representation of n.
3
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
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
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, Apr 14 2015
STATUS
approved