A100926 Number of partitions of n into parts free of odd squares and the only number with multiplicity in the unrestricted partitions is the number 2.
1, 0, 1, 1, 2, 2, 3, 4, 5, 6, 8, 10, 12, 15, 18, 23, 27, 33, 40, 48, 57, 69, 81, 97, 113, 134, 157, 184, 214, 250, 290, 337, 389, 451, 519, 598, 688, 789, 904, 1035, 1181, 1348, 1535, 1746, 1983, 2250, 2549, 2885, 3261, 3682, 4154, 4680, 5268, 5923, 6656, 7468
Offset: 1
Keywords
Examples
a(10)=8 because 10 =8+2 =7+3 =6+4 =5+3+2 =6+2+2 =4+2+2+2 =2+2+2+2+2.
Links
- Noureddine Chair, Partition Identities From Partial Supersymmetry, arXiv:hep-th/0409011v1, 2004.
- James A. Sellers, Partitions Excluding Specific Polygonal Numbers As Parts, Journal of Integer Sequences, Vol. 7 (2004), Article 04.2.4.
Programs
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Maple
series(product((1+x^k)/(1-(-1)^k*x^(k^2)),k=1..100),x=0,100);
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Mathematica
terms = 56; Product[(1 + x^k)/(1 - (-1)^k*x^(k^2)), {k, 1, terms}] + O[x]^terms // CoefficientList[#, x]& (* Jean-François Alcover, Dec 14 2018 *)
Formula
G.f.: Product_{k>=0}(1+x^k)/(1-(-1)^k*x^(k^2)).
Comments