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A339405 Number of partitions of n into an odd number of parts that are not multiples of 3. 3
0, 1, 1, 1, 2, 3, 3, 5, 6, 8, 11, 14, 17, 23, 28, 35, 44, 55, 66, 83, 100, 122, 148, 179, 213, 259, 307, 366, 436, 518, 609, 723, 848, 997, 1169, 1369, 1593, 1864, 2163, 2513, 2914, 3376, 3894, 4503, 5182, 5965, 6854, 7869, 9008, 10325, 11794, 13470, 15363, 17509, 19911, 22654, 25713, 29177 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,5

LINKS

Table of n, a(n) for n=0..57.

Index entries for sequences related to partitions

FORMULA

G.f.: (1/2) * (Product_{k>=1} (1 - x^(3*k)) / (1 - x^k) - Product_{k>=1} (1 + x^(3*k)) / (1 + x^k)).

a(n) = (A000726(n) - A109389(n)) / 2.

EXAMPLE

a(7) = 5 because we have [7], [5, 1, 1], [4, 2, 1], [2, 2, 1, 1, 1] and [1, 1, 1, 1, 1, 1, 1].

MAPLE

b:= proc(n, i, t) option remember; `if`(n=0, t, `if`(i<1, 0,

      b(n, i-1, t)+`if`(irem(i, 3)=0, 0, b(n-i, min(n-i, i), 1-t))))

    end:

a:= n-> b(n$2, 0):

seq(a(n), n=0..60);  # Alois P. Heinz, Dec 03 2020

MATHEMATICA

nmax = 57; CoefficientList[Series[(1/2) (Product[(1 - x^(3 k))/(1 - x^k), {k, 1, nmax}] - Product[(1 + x^(3 k))/(1 + x^k), {k, 1, nmax}]), {x, 0, nmax}], x]

CROSSREFS

Cf. A000726, A001651, A027193, A109389, A339404, A339406, A339407.

Sequence in context: A107236 A192184 A027586 * A039860 A084338 A300446

Adjacent sequences:  A339402 A339403 A339404 * A339406 A339407 A339408

KEYWORD

nonn

AUTHOR

Ilya Gutkovskiy, Dec 03 2020

STATUS

approved

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Last modified April 21 12:24 EDT 2021. Contains 343150 sequences. (Running on oeis4.)