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A086159
Number of partitions of n into the first three triangular numbers, 1, 3 and 6.
0
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
Jan Snellman and Michael Paulsen, Enumeration of Concave Integer Partitions, J. Integer Seq., Vol. 7 (2004), Article 04.1.3.
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
Sequence in context: A079438 A123050 A113694 * A029048 A376179 A086160
KEYWORD
nonn
AUTHOR
Jan Snellman (Jan.Snellman(AT)math.su.se), Aug 25 2003
STATUS
approved