0,2

Number of partitions of n into distinct parts prime to 3, with 2 types of each part.

This is also the number of partitions of n into parts with 2 types congruent to 1 or 5 mod(6).

Noureddine Chair, Partitions Identities From Partial Supersymmetry.

D. Ford, J. McKay and S. P. Norton, More on replicable functions, Commun. Algebra 22, No. 13, 5175-5193 (1994).

Index entries for McKay-Thompson series for Monster simple group

G.f.: product_{k>0}((1+x^k)/(1+x^(3k)))^2= 1/product_{k>0}((1-x^(6k-1))*(1-x^(6k-5)))^2.

Expansion of q^(1/6)(eta(q^2)eta(q^3)/(eta(q)eta(q^6)))^2 in powers of q.

Euler transform of period 6 sequence [2, 0, 0, 0, 2, 0, ...]. - Michael Somos Sep 10 2005

E.g. a(5)=8 because we have 5,5*,41,41*,4*1,4*1*,22*1,22*1* with all parts prime to 3. The parts congruent to 1,5 mod(6) are,5,5*,11111,11111*,1111*1*,111*1*1*,11*1*1*1*,1*1*1*1*1*

T36g = 1/q +2*q^5 +3*q^11 +4*q^17 +5*q^23 +8*q^29 +11*q^35 +...

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

CoefficientList[ Series[ Product[(1 + x^k)^2/(1 + x^(3k))^2, {k, 60}], {x, 0, 50}], x] (from Robert G. Wilson v Feb 22 2005)

(PARI) {a(n)=local(A); if(n<0, 0, A=x*O(x^n); polcoeff( (eta(x^2+A)*eta(x^3+A)/eta(x+A)/eta(x^6+A))^2, n))} /* Michael Somos Sep 10 2005 */

Cf. A003105.

Sequence in context: A144679 A008825 A078762 this_sequence A135318 A101137 A053021

Adjacent sequences: A103259 A103260 A103261 this_sequence A103263 A103264 A103265

nonn

Noureddine Chair (n.chair(AT)rocketmail.com), Feb 21 2005

More terms from Robert G. Wilson v (rgwv(AT)rgwv.com), Feb 22 2005