A081055 Number of partitions of 2n in which no parts are multiples of 4.

1, 2, 4, 9, 16, 29, 50, 82, 132, 208, 320, 484, 722, 1060, 1539, 2210, 3138, 4416, 6163, 8528, 11716, 15986, 21666, 29190, 39104, 52098, 69060, 91106, 119634, 156416, 203664, 264128, 341256, 439321, 563600, 720648, 918530, 1167154, 1478720

Offset: 0

Author

Michael Somos, Mar 03 2003

Keywords

• nonn
• easy

Comments

Euler transform of period 16 sequence [2,1,3,1,3,0,2,0,2,0,3,1,3,1,2,0,...].

Links

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

Crossrefs

Cf. A001935, A074378, A081056.

Programs

Mathematica

Table[Count[IntegerPartitions[2n], x_ /; ! MemberQ [Mod[x, 4], 0, 2] ], {n, 0, 38}] (* Robert Price, Jul 28 2020 *)

PARI

a(n)=local(X); if(n<0,0,X=x+x*O(x^(2*n)); polcoeff(eta(X^4)/eta(X),2*n))

Formula

G.f.: (sum_{n>=0} x^A074378(n))/(sum_n (-x)^n^2).

a(n) = A001935(2n).

a(n) ~ exp(Pi*sqrt(n)) / (2^(7/2) * n^(3/4)). - Vaclav Kotesovec, Nov 15 2017