A369341 Number of compositions (ordered partitions) of n into triangular numbers not greater than sqrt(n).

1, 1, 1, 1, 1, 1, 1, 1, 1, 19, 28, 41, 60, 88, 129, 189, 277, 406, 595, 872, 1278, 1873, 2745, 4023, 5896, 8641, 12664, 18560, 27201, 39865, 58425, 85626, 125491, 183916, 269542, 395033, 2823330, 4343681, 6682741, 10281375, 15817857, 24335721, 37440426, 57601964

Offset

0,10

Links

Table of n, a(n) for n=0..43.

Mathematica

Table[SeriesCoefficient[1/(1 - Sum[x^(k (k + 1)/2), {k, 1, Floor[(Sqrt[1 + 8 Sqrt[n]] - 1)/2]}]), {x, 0, n}], {n, 0, 43}]

Crossrefs

Cf. A023361, A364526.

Sequence in context: A083678 A279771 A257043 * A368871 A120144 A255924

Adjacent sequences: A369338 A369339 A369340 * A369342 A369343 A369344

Keyword

nonn

Author

Ilya Gutkovskiy, Jan 20 2024

Status

approved