The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A320607 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A320607

Number of parts in all partitions of n in which no part occurs more than four times.
(history; published version)

#12 by Harvey P. Dale at Mon May 18 20:21:16 EDT 2020

STATUS

editing

approved

#11 by Harvey P. Dale at Mon May 18 20:21:12 EDT 2020

MATHEMATICA

Table[Length[Flatten[Select[IntegerPartitions[n], Max[Tally[#][[All, 2]]]<5&]]], {n, 50}] (* Harvey P. Dale, May 18 2020 *)

STATUS

approved

editing

#10 by Vaclav Kotesovec at Thu Oct 18 10:19:11 EDT 2018

STATUS

editing

approved

#9 by Vaclav Kotesovec at Thu Oct 18 09:16:00 EDT 2018

FORMULA

a(n) ~ 3^(1/4) * log(5) * exp(2*Pi*sqrt(2*n/15)) / (2^(5/4) * 5^(1/4) * Pi * n^(1/4)). - Vaclav Kotesovec, Oct 18 2018

STATUS

approved

editing

#8 by Alois P. Heinz at Wed Oct 17 16:11:35 EDT 2018

STATUS

editing

approved

#7 by Alois P. Heinz at Wed Oct 17 16:10:46 EDT 2018

CROSSREFS

Cf. A035959.

STATUS

approved

editing

#6 by Alois P. Heinz at Wed Oct 17 11:33:45 EDT 2018

STATUS

editing

approved

#5 by Alois P. Heinz at Wed Oct 17 11:33:42 EDT 2018

LINKS

Alois P. Heinz, <a href="/A320607/b320607.txt">Table of n, a(n) for n = 1..5000</a>

MAPLE

b:= proc(n, i) option remember; `if`(n=0, [1, 0], `if`(42*i*(i+1)/2<n, 0, add(

0, add((l-> [0, l[1]*j]+l)(b(n-i*j, min(n-i*j, i-1)), ), j=0..min(n/i, 4))))

#4 by Alois P. Heinz at Wed Oct 17 10:32:43 EDT 2018

MAPLE

b:= proc(n, i) option remember; `if`(n=0, [1, 0], `if`(4*i*(i+1)/2<n,

0, add((l-> [0, l[1]*j]+l)(b(n-i*j, i-1)), j=0..min(n/i, 4))))

end:

a:= n-> b(n$2)[2]:

seq(a(n), n=1..50);

#3 by Alois P. Heinz at Wed Oct 17 10:24:24 EDT 2018

NAME

allocated for Alois P. Heinz

Number of parts in all partitions of n in which no part occurs more than four times.

DATA

1, 3, 6, 12, 15, 29, 41, 65, 91, 132, 179, 257, 339, 465, 616, 823, 1062, 1402, 1790, 2320, 2939, 3750, 4701, 5946, 7398, 9243, 11428, 14161, 17368, 21372, 26056, 31823, 38596, 46838, 56499, 68208, 81868, 98292, 117489, 140390, 167068, 198796, 235655, 279239

OFFSET

1,2

CROSSREFS

Column k=4 of A210485.

KEYWORD

allocated

nonn

AUTHOR

Alois P. Heinz, Oct 17 2018

STATUS

approved

editing