A253144 Number of partitions of n into distinct parts congruent to 1, 2, or 4 modulo 6.

1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 3, 3, 3, 4, 5, 5, 5, 6, 6, 7, 9, 10, 11, 12, 13, 14, 16, 18, 19, 21, 23, 25, 28, 31, 34, 37, 40, 43, 47, 52, 56, 61, 66, 71, 78, 85, 92, 99, 107, 115, 124, 135, 145, 156, 168, 180, 194, 210, 226, 242, 260, 278, 297, 320, 343, 367, 393, 420, 449, 481, 516, 550, 587, 626, 666, 712, 760, 810, 863, 919, 978, 1041, 1110, 1180, 1254, 1333, 1414, 1503, 1598, 1697, 1801

Offset: 0

Author

Jeremy Lovejoy, Mar 23 2015

Keywords

• nonn

Comments

a(n) is also the number of partitions of n into parts congruent to 1, 7, or 10 modulo 12.

a(n) is also the number of partitions of n into parts that differ by at least 6, where the inequality is strict if the larger part is 0, 3, or 5 modulo 6, with the exception that 6+1 may appear.

Examples

			a(14) = 5, the valid partitions being 14, 13+1, 10+4, 8+4+2, and 7+4+2+1.
		

Links

• Robert Israel, Table of n, a(n) for n = 0..10000
• K. Alladi and G. E. Andrews, The dual of Göllnitz's (big) partition theorem, Ramanujan J. 36 (2015), 171-201.

Crossrefs

Cf. A056970.

Programs

Maple

series(mul((1+x^(6*k+1))*(1+x^(6*k+2))*(1+x^(6*k+4)),k=0..100),x=0,100)

Formula

a(n) ~ exp(sqrt(n/6)*Pi) / (2^(17/12) * 3^(1/4) * n^(3/4)). - Vaclav Kotesovec, May 24 2018