1,4

Also, number of partitions of in which the distinct parts are prime to 3 and the unrestricted parts are multiples of 3.

The inverted graded parafermionic partition function. This g.f. is a generalization of A003105, A006950 and A096938

T. M. Apostol, An Introduction to Analytic Number Theory, Springer-Verlag, NY, 1976

Noureddine Chair, Partition identities from partial supersymmetry.

D. Spector, Duality, partial supersymmetry and arithmetic number theory, J. Math. Phys. vol. 39, 1998, p. 1919.

Euler transform of period 6 sequence [1, 0, 1, 0, 1, 1, ...]. - Vladeta Jovovic (vladeta(AT)eunet.rs), Aug 20 2004

G.f.: 1/product_{k>=1}(1-x^k+x^(2*k)-x^(3*k)+x^(4*k)-x^(5*k))=Product_{k>=1}(1+X^(3*k-1))(1+x^(3*k-2))/(1-x^(3*k))

E.g. a(11) = 15 because we can write 11 = 10+1 = 8+2+1 = 7+4 = 5+4+2 (parts do not not contain multiple of 3) = 9+2 = 8+3 = 7+3+1 = 6+5 = 6+4+1 = 6+3+2 = 5+3+3 = 5+3+2+1 = 4+3+3+1 = 3+3+3+2

series(product(1/(1-x^k+x^(2*k)-x^(3*k)+x^(4*k)-x^(5*k)), k=1..150), x=0, 100);

CoefficientList[ Series[ Product[ 1/(1 - x^k + x^(2k) - x^(3k) + x^(4k) - x^(5k)), {k, 55}], {x, 0, 53}], x] (from Robert G. Wilson v Aug 21 2004)

Sequence in context: A098180 A117752 A006065 this_sequence A035541 A060966 A135279

Adjacent sequences: A096978 A096979 A096980 this_sequence A096982 A096983 A096984

nonn

Noureddine Chair (n.chair(AT)rocketmail.com), Aug 19 2004

Better definition from Vladeta Jovovic (vladeta(AT)eunet.rs), Aug 20 2004

More terms from Robert G. Wilson v (rgwv(AT)rgwv.com), Aug 21 2004