A086159 Number of partitions of n into the first three triangular numbers, 1, 3 and 6.

1, 1, 1, 2, 2, 2, 4, 4, 4, 6, 6, 6, 9, 9, 9, 12, 12, 12, 16, 16, 16, 20, 20, 20, 25, 25, 25, 30, 30, 30, 36, 36, 36, 42, 42, 42, 49, 49, 49, 56, 56, 56, 64, 64, 64, 72, 72, 72, 81, 81, 81, 90, 90, 90, 100, 100, 100, 110, 110, 110, 121, 121, 121, 132, 132, 132

Offset: 0

Author

Jan Snellman, Aug 25 2003

Keywords

• nonn

Links

• Jan Snellman and Michael Paulsen, Enumeration of Concave Integer Partitions, J. Integer Seq., Vol. 7 (2004), Article 04.1.3.
• Index entries for linear recurrences with constant coefficients, signature (1,0,1,-1,0,1,-1,0,-1,1).

Crossrefs

Cf. A000217, A008620.

Programs

Mathematica

LinearRecurrence[{1, 0, 1, -1, 0, 1, -1, 0, -1, 1}, {1, 1, 1, 2, 2, 2, 4, 4, 4, 6}, 100] (* Amiram Eldar, Feb 14 2023 *)

Formula

G.f.: 1/((1-x)*(1-x^3)*(1-x^6)).

Sum_{n>=0} 1/a(n) = Pi^2/2 + 3. - Amiram Eldar, Feb 14 2023