A036022 - OEIS

%I #11 May 09 2018 10:09:07

%S 1,1,1,2,3,3,4,6,8,10,12,15,20,24,28,36,45,53,63,77,93,110,129,154,

%T 185,216,251,297,350,405,469,548,638,736,846,978,1131,1295,1480,1701,

%U 1951,2222,2529,2886,3288,3730,4224,4793,5436,6138,6921,7819,8823,9922,11150

%N Number of partitions of n into parts not of form 4k+2, 16k, 16k+5 or 16k-5.

%C Case k=4,i=3 of Gordon/Goellnitz/Andrews Theorem.

%C Also number of partitions in which no odd part is repeated, with at most 2 parts of size less than or equal to 2 and where differences between parts at distance 3 are greater than 1 when the larger part is odd and greater than 2 when the larger part is even.

%C Euler transform of period 16 sequence [1,0,1,1,0,0,1,1,1,0,0,1,1,0,1,0,...]. - _Michael Somos_, Jul 15 2004

%D G. E. Andrews, The Theory of Partitions, Addison-Wesley, 1976, p. 114.

%F a(n) ~ 3^(1/4) * sqrt(2 + sqrt(2 - sqrt(2))) * exp(sqrt(3*n/2)*Pi/2) / (2^(15/4) * n^(3/4)). - _Vaclav Kotesovec_, May 09 2018

%o (PARI) a(n)=if(n<0,0,polcoeff(1/prod(k=1,n,1-([1,0,1,1,0,0,1,1,1,0,0,1,1,0,1,0][(k-1)%16+1])*x^k,1+x*O(x^n)),n))

%K nonn,easy

%O 0,4

%A _Olivier Gérard_