A035592 Number of partitions of 3n with same number of parts == 1 (mod 3) and == 2 (mod 3).

1, 2, 6, 14, 32, 66, 134, 256, 480, 868, 1540, 2664, 4536, 7574, 12474, 20234, 32428, 51324, 80388, 124582, 191310, 291114, 439394, 657936, 978054, 1443684, 2117136, 3085174, 4469368, 6437742, 9223324, 13145792, 18644484, 26317916, 36981828

Offset: 0

Author

Olivier Gérard

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..1000
• Mircea Merca, Truncated forms of MacMahon's q-series, Journal of Combinatorial Theory, Series A, Volume 213, 106020 (2025). See p. 8.

Crossrefs

Cf. A035536.

Programs

PARI

{a(n) = if( n<0, 0, polcoeff( sum( k=0,(sqrtint(1 + 8*n) - 1)\2, (-1)^k * x^((k+k^2)/2)) / eta(x + x * O(x^n))^3, n))} /* Michael Somos, Jul 28 2003 */

Formula

a(n) = A035536(3*n).

G.f.: (Sum_{k>=0} (-1)^k * x^(k * (k + 1)/2)) / (Product_{k>0} 1 - x^k)^3. - Michael Somos, Jul 28 2003

Extensions

More terms from David W. Wilson