A348529 Number of compositions (ordered partitions) of n into two or more triangular numbers.

0, 0, 1, 1, 3, 4, 6, 11, 16, 25, 39, 61, 94, 147, 227, 350, 546, 846, 1309, 2030, 3147, 4875, 7558, 11715, 18154, 28136, 43609, 67586, 104747, 162346, 251610, 389958, 604381, 936699, 1451743, 2249991, 3487152, 5404570, 8376292, 12982016, 20120202, 31183350, 48329596, 74903735

Offset

0,5

Links

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

Formula

a(n) = A023361(n) - A010054(n). - Alois P. Heinz, Oct 21 2021

Maple

b:= proc(n) option remember; `if`(n=0, 1, add(
     `if`(issqr(8*j+1), b(n-j), 0), j=1..n))
    end:
a:= n-> b(n)-`if`(issqr(8*n+1), 1, 0):
seq(a(n), n=0..43);  # Alois P. Heinz, Oct 21 2021

Mathematica

b[n_] := b[n] = If[n == 0, 1, Sum[
     If[IntegerQ@ Sqrt[8*j + 1], b[n - j], 0], {j, 1, n}]];
a[n_] := b[n] - If[IntegerQ@ Sqrt[8*n + 1], 1, 0];
Table[a[n], {n, 0, 43}] (* Jean-François Alcover, Mar 01 2022, after Alois P. Heinz *)

Crossrefs

Cf. A000217, A010054, A023361, A347805, A348526, A348528.

Sequence in context: A230430 A154331 A001130 * A069825 A093040 A022935

Adjacent sequences: A348526 A348527 A348528 * A348530 A348531 A348532

Keyword

nonn

Author

Ilya Gutkovskiy, Oct 21 2021

Status

approved