This site is supported by donations to The OEIS Foundation.

 Please make a donation to keep the OEIS running. We are now in our 55th year. In the past year we added 12000 new sequences and reached 8000 citations (which often say "discovered thanks to the OEIS"). We need to raise money to hire someone to manage submissions, which would reduce the load on our editors and speed up editing. Other ways to donate

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 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 (list; graph; refs; listen; history; text; internal format)
 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), 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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified December 6 19:22 EST 2019. Contains 329809 sequences. (Running on oeis4.)