login
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.
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
1,5
COMMENTS
This is also the inverted graded generating function for the number of partitions in which no square parts are present
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.
FORMULA
G.f.: Product_{k>=0}(1+x^k)/(1-(-1)^k*x^(k^2)).
EXAMPLE
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.
MAPLE
series(product((1+x^k)/(1-(-1)^k*x^(k^2)), k=1..100), x=0, 100);
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 *)
CROSSREFS
Sequence in context: A117409 A092833 A280664 * A351008 A258875 A179241
KEYWORD
nonn
AUTHOR
Noureddine Chair, Nov 22 2004
STATUS
approved