

A253144


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


1



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
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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 GĂ¶llnitz's (big) partition theorem, Ramanujan J. 36 (2015), 171201.


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



