A301507 Expansion of Product_{k>=0} (1 + x^(4*k+1))*(1 + x^(4*k+2)).

1, 1, 1, 1, 0, 1, 2, 2, 2, 2, 2, 3, 3, 3, 4, 5, 6, 6, 6, 7, 8, 9, 10, 11, 13, 14, 14, 16, 18, 20, 23, 24, 27, 30, 31, 34, 37, 41, 46, 49, 53, 58, 62, 67, 73, 80, 88, 94, 101, 109, 117, 127, 136, 147, 161, 172, 184, 198, 211, 228, 245, 262, 284, 304, 324, 347, 370, 397, 425, 454, 488

Offset

0,7

Comments

Number of partitions of n into distinct parts congruent to 1 or 2 mod 4.

Links

Table of n, a(n) for n=0..70.

Index entries for sequences related to partitions

Formula

G.f.: Product_{k>=1} (1 + x^A042963(k)).

a(n) ~ exp(Pi*sqrt(n/6)) / (2^(3/2)*3^(1/4)*n^(3/4)). - Vaclav Kotesovec, Mar 23 2018

Example

a(11) = 3 because we have [10, 1], [9, 2] and [6, 5].

Mathematica

nmax = 70; CoefficientList[Series[Product[(1 + x^(4 k + 1)) (1 + x^(4 k + 2)), {k, 0, nmax}], {x, 0, nmax}], x]
nmax = 70; CoefficientList[Series[QPochhammer[-x, x^4] QPochhammer[-x^2, x^4], {x, 0, nmax}], x]
nmax = 70; CoefficientList[Series[Product[(1 + Boole[MemberQ[{1, 2}, Mod[k, 4]]] x^k), {k, 1, nmax}], {x, 0, nmax}], x]

Crossrefs

Cf. A035365, A042963, A070048, A108932, A169975, A301504, A301505, A301508.

Sequence in context: A280951 A120202 A141053 * A005861 A238457 A291310

Adjacent sequences: A301504 A301505 A301506 * A301508 A301509 A301510

Keyword

nonn

Author

Ilya Gutkovskiy, Mar 22 2018

Status

approved