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

0,4

Links

Table of n, a(n) for n=0..65.

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).

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

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 *)

Crossrefs

Cf. A000217, A008620.

Sequence in context: A079438 A123050 A113694 * A029048 A086160 A029047

Adjacent sequences: A086156 A086157 A086158 * A086160 A086161 A086162

Keyword

nonn

Author

Jan Snellman (Jan.Snellman(AT)math.su.se), Aug 25 2003

Status

approved