The On-Line Encyclopedia of Integer Sequences (OEIS)

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A339222

Number of partitions of n into parts >= 2 where every part appears at least 2 times.
(history; published version)

#7 by Vaclav Kotesovec at Wed Dec 09 04:18:20 EST 2020

STATUS

editing

approved

#6 by Vaclav Kotesovec at Wed Dec 09 04:18:13 EST 2020

LINKS

Vaclav Kotesovec, <a href="/A339222/b339222.txt">Table of n, a(n) for n = 0..10000</a>

#5 by Vaclav Kotesovec at Wed Dec 09 03:56:58 EST 2020

FORMULA

a(n) ~ exp(2*Pi*sqrt(n)/3) * Pi / (18*sqrt(2)*n^(3/2)). - Vaclav Kotesovec, Dec 09 2020

STATUS

approved

editing

#4 by Susanna Cuyler at Sat Nov 28 09:12:37 EST 2020

STATUS

proposed

approved

#3 by Ilya Gutkovskiy at Fri Nov 27 18:34:24 EST 2020

STATUS

editing

proposed

#2 by Ilya Gutkovskiy at Fri Nov 27 18:22:21 EST 2020

NAME

allocated for Ilya GutkovskiyNumber of partitions of n into parts >= 2 where every part appears at least 2 times.

DATA

1, 0, 0, 0, 1, 0, 2, 0, 2, 1, 3, 0, 6, 1, 6, 3, 10, 2, 15, 4, 18, 9, 25, 8, 38, 14, 44, 24, 62, 26, 86, 39, 105, 61, 139, 70, 191, 100, 230, 144, 304, 173, 400, 235, 490, 326, 629, 395, 819, 525, 996, 701, 1269, 859, 1617, 1114, 1974, 1456, 2475, 1783, 3124, 2279, 3793, 2920

OFFSET

0,7

LINKS

<a href="/index/Par#part">Index entries for sequences related to partitions</a>

FORMULA

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

EXAMPLE

a(12) = 6 because we have [6, 6], [4, 4, 4], [4, 4, 2, 2], [3, 3, 3, 3], [3, 3, 2, 2, 2] and [2, 2, 2, 2, 2, 2].

MATHEMATICA

nmax = 63; CoefficientList[Series[Product[1 + x^(2 k)/(1 - x^k), {k, 2, nmax}], {x, 0, nmax}], x]

CROSSREFS

Cf. A002865, A007690.

KEYWORD

allocated

nonn

AUTHOR

Ilya Gutkovskiy, Nov 27 2020

STATUS

approved

editing

#1 by Ilya Gutkovskiy at Fri Nov 27 18:22:21 EST 2020

NAME

allocated for Ilya Gutkovskiy

KEYWORD

allocated

STATUS

approved