A081056 Number of partitions of 2n+1 in which no parts are multiples of 4.

1, 3, 6, 12, 22, 38, 64, 105, 166, 258, 395, 592, 876, 1280, 1846, 2636, 3728, 5222, 7256, 10006, 13696, 18624, 25169, 33808, 45164, 60022, 79366, 104457, 136870, 178572, 232044, 300368, 387366, 497804, 637568, 813910, 1035792, 1314214

Offset

0,2

Comments

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

Links

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

Formula

G.f.: (sum_{n>=0} x^A074377(n))/(sum_n (-x)^n^2).

a(n) = A001935(2n+1).

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

Mathematica

Table[Count[IntegerPartitions[2n+1], _?(Total[Boole[Divisible[#, 4]]]==0&)], {n, 0, 40}] (* Harvey P. Dale, Sep 11 2019 *)

Prog

(PARI) a(n)=local(X); if(n<0, 0, X=x+x^2*O(x^(2*n)); polcoeff(eta(X^4)/eta(X), 2*n+1))

Crossrefs

Cf. A001935, A074377, A081055.

Sequence in context: A062483 A174013 A309266 * A242448 A066982 A246597

Adjacent sequences: A081053 A081054 A081055 * A081057 A081058 A081059

Keyword

nonn,easy

Author

Michael Somos, Mar 03 2003

Status

approved