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A081056 Number of partitions of 2n+1 in which no parts are multiples of 4. 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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified October 15 20:04 EDT 2019. Contains 328037 sequences. (Running on oeis4.)