A033792 Product t2(q^d); d | 33, where t2(q) = theta2(q)/(2*q^(1/4)).

1, 1, 0, 2, 1, 0, 2, 0, 0, 2, 2, 1, 2, 1, 2, 3, 0, 2, 2, 2, 2, 4, 0, 1, 4, 0, 2, 0, 2, 2, 4, 2, 2, 4, 2, 3, 6, 3, 0, 8, 1, 2, 6, 4, 3, 7, 4, 4, 8, 0, 4, 7, 4, 2, 8, 2, 5, 9, 2, 4, 1, 4, 4, 8, 6, 4, 12, 2, 3, 12, 4, 1, 10, 5, 4, 10, 4, 6, 12, 6, 4, 11, 0, 2, 15, 6

Offset

0,4

Comments

The above function t2 simplifies to t2(z) = 1 + z^2 + z^6 + z^12 + ... = sum_{n>=0} z^(n(n+1)) = sum_{n>=0} z^A002378(n). But the sequence lists only the coefficients of even powers, i.e., with t2 replaced by t(z) = 1 + z + z^3 + z^6 + ..., cf. formula. - M. F. Hasler, Oct 17 2014

Links

Seiichi Manyama, Table of n, a(n) for n = 0..10000

Formula

Coefficients of product_{d|33} t(x^d), with t(z) = sum_{n>=0} z^(n(n+1)/2) = sum_{n>=0} z^A000217(n). - M. F. Hasler, Oct 17 2014

Prog

(PARI) my(x='x+O('x^99), t(z)=sum(i=0, 10, z^((i+1)*i/2))); Vec(prod(i=1, #d=divisors(33), t(x^d[i]))) \\ M. F. Hasler, Oct 17 2014

Crossrefs

Sequence in context: A033762 A129449 A033798 * A033768 A033786 A366768

Adjacent sequences: A033789 A033790 A033791 * A033793 A033794 A033795

Keyword

nonn

Author

N. J. A. Sloane

Extensions

More terms from Seiichi Manyama, May 24 2017

Status

approved