The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A036017 Number of partitions of n into parts not of form 4k+2, 12k, 12k+1 or 12k-1. 0
 1, 0, 0, 1, 1, 1, 1, 2, 3, 3, 3, 4, 6, 6, 7, 10, 12, 13, 15, 19, 23, 26, 29, 36, 44, 48, 54, 66, 77, 86, 98, 115, 134, 150, 169, 197, 227, 253, 285, 329, 375, 418, 470, 536, 607, 678, 757, 858, 969, 1076, 1200, 1353, 1516, 1683, 1873, 2098, 2343, 2596, 2878, 3211 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,8 COMMENTS Case k=3,i=1 of Gordon/Goellnitz/Andrews Theorem. Also number of partitions in which no odd part is repeated, with no part of size less than or equal to 2 and where differences between parts at distance 2 are greater than 1 when the larger part is odd and greater than 2 when the larger part is even. Euler transform of period 12 sequence [0,0,1,1,1,0,1,1,1,0,0,0,...]. - Michael Somos, Jun 28 2004 REFERENCES G. E. Andrews, The Theory of Partitions, Addison-Wesley, 1976, p. 114. LINKS FORMULA a(n) ~ exp(Pi*sqrt(n/3)) * sqrt(2*sqrt(3) - 3) / (12 * n^(3/4)). - Vaclav Kotesovec, May 10 2018 MATHEMATICA nmax = 60; CoefficientList[Series[Product[(1 - x^(4*k - 2))*(1 - x^(12*k))*(1 - x^(12*k+1-12))*(1 - x^(12*k- 1))/(1 - x^k), {k, 1, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, May 10 2018 *) PROG (PARI) {a(n)=if(n<0, 0, polcoeff(1/prod(k=1, n, 1-([0, 0, 1, 1, 1, 0, 1, 1, 1, 0, 0, 0][(k-1)%12+1])*x^k, 1+x*O(x^n)), n))} /* Michael Somos, Jun 28 2004 */ CROSSREFS Sequence in context: A108932 A029067 A048460 * A029066 A174522 A327719 Adjacent sequences:  A036014 A036015 A036016 * A036018 A036019 A036020 KEYWORD nonn,easy AUTHOR 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 September 23 12:06 EDT 2021. Contains 347616 sequences. (Running on oeis4.)