Search: id:A036020
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%I A036020
%S A036020 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 A036020 101,114,131,155,182,206,234,275,319,359,408,474,544,612,694,797,909,
%U A036020 1023,1153,1315,1494,1673,1881,2134,2407,2693,3019,3403,3825,4269,4768
%N A036020 Number of partitions of n into parts not of form 4k+2, 16k, 16k+1 or 
               16k-1.
%C A036020 Case k=4,i=1 of Gordon/Goellnitz/Andrews Theorem.
%C A036020 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 A036020 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 A036020 G. E. Andrews, The Theory of Partitions, Addison-Wesley, 1976, p. 114.
%o A036020 (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))
%Y A036020 Sequence in context: A162157 A060210 A000025 this_sequence A036024 A036029 
               A035362
%Y A036020 Adjacent sequences: A036017 A036018 A036019 this_sequence A036021 A036022 
               A036023
%K A036020 nonn,easy
%O A036020 0,8
%A A036020 Olivier Gerard (olivier.gerard(AT)gmail.com)

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