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

0,2

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

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

Mathematica

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

Prog

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

Crossrefs

Cf. A001935, A074378, A081056.

Sequence in context: A333779 A261240 A000291 * A034446 A174511 A034452

Adjacent sequences: A081052 A081053 A081054 * A081056 A081057 A081058

Keyword

nonn,easy

Author

Michael Somos, Mar 03 2003

Status

approved