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%I #11 May 09 2018 10:04:44
%S 1,0,0,1,1,1,1,2,3,3,3,5,7,7,8,11,14,15,18,23,28,32,36,45,55,61,70,86,
%T 101,114,131,155,182,206,234,275,319,359,408,474,544,612,694,797,909,
%U 1023,1153,1315,1494,1673,1881,2134,2407,2693,3019,3403,3825,4269,4768
%N Number of partitions of n into parts not of form 4k+2, 16k, 16k+1 or 16k-1.
%C Case k=4,i=1 of Gordon/Goellnitz/Andrews Theorem.
%C 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 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 [0,0,1,1,1,0,1,1,1,0,1,1,1,0,0,0,...]. - _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-([0,0,1,1,1,0,1,1,1,0,1,1,1,0,0,0][(k-1)%16+1])*x^k,1+x*O(x^n)),n))
%K nonn,easy
%O 0,8
%A _Olivier Gérard_
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