A100928 - OEIS

%I #12 Jan 27 2019 09:54:18

%S 1,0,1,1,1,2,2,3,4,5,6,8,9,12,14,18,21,26,31,37,44,52,62,73,86,101,

%T 118,138,160,186,216,249,288,332,381,438,501,573,655,746,851,966,1099,

%U 1244,1410,1595,1801,2033,2292,2580,2903,3261,3660,4105,4598,5147,5755

%N Number of partitions of n into parts free of odd octagonal (star) numbers: k(3k-2) and the only number with multiplicity in the unrestricted partitions is the number 2 with multiplicity of the form :4k+2l, k a positive integer and l=0,1.

%C This is also the inverted graded of the generating function for partitions of n into parts free of octagonal numbers.

%H Noureddine Chair, <a href="http://arxiv.org/abs/hep-th/0409011">Partition Identities From Partial Supersymmetry</a>, arXiv:hep-th/0409011v1, 2004.

%H James A. Sellers, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL7/Sellers/sellers58.html">Partitions Excluding Specific Polygonal Numbers As Parts</a>, Journal of Integer Sequences, Vol. 7 (2004), Article 04.2.4.

%F G.f.: product_{k>0}(1+x^k)/(1-(-1)^k*x^(3*k^2-2k)).

%e a(15)=18 because 15 =13+5 =12+3 =11+4 =10+5 =10+3+2 =9+6 =9+4+2 =8+7 =8+4+3 =8+5+2 =7+6+2 =7+5+3 =6+5+4 =6+4+3+2 =5+2+2+2+2+2 =7+2+2+2+2 =4+3+2+2+2+2.

%p series(product((1+x^k)/(1-(-1)^k*x^(3*k^(2)-2*k)),k=1..100),x=0,100);

%K nonn

%O 1,6

%A _Noureddine Chair_, Nov 23 2004