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

0,8

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.

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.

Formula

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

Example

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

Maple

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

Crossrefs

Cf. A056970.

Sequence in context: A029062 A219502 A219704 * A265410 A029249 A025770

Adjacent sequences: A253141 A253142 A253143 * A253145 A253146 A253147

Keyword

nonn

Author

Jeremy Lovejoy, Mar 23 2015

Status

approved