A258257 The number of representations of n as a minimal number of triangular numbers, A000217(n).

1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 1, 2, 1, 1, 1, 2, 1, 1, 2, 1, 1, 1, 1, 2, 2, 2, 1, 2, 1, 1, 1, 1, 3, 2, 2, 1, 2, 1, 2, 2, 1, 1, 1, 2, 5, 1, 2, 1, 2, 1, 1, 3, 1, 1, 2, 3, 1, 1, 1, 1, 2, 1, 1, 3, 2, 1, 2, 4, 2, 3, 1, 1, 2, 3, 6, 1, 1, 3, 3, 1

Offset: 1

Author

Martin Renner, May 24 2015

Keywords

• nonn

Examples

			a(5) = 1 since 5 = 1 + 1 + 3 is the only representation as a minimal number of three triangular numbers.
a(16) = 2 since 16 = 1 + 15 = 6 + 10 has two representations as a minimal number of two triangular numbers.
		

Links

• Giovanni Resta, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A061336, A180466.

Programs

Mathematica

t[n_] := n (n + 1)/2; a[n_] := Block[{k = 1, t, tt = t /@ Range[ Sqrt[2*n]]}, While[{} == (r = IntegerPartitions[n, {k}, tt]), k++]; Length@r]; Array[a, 100] (* Giovanni Resta, Jun 09 2015 *)