A087183 -id:A087183 - cp's OEIS frontend

A087180 Number partition numbers <= P(n) of the form 3*k (P = A000041).

0, 0, 0, 1, 1, 1, 1, 2, 2, 3, 4, 4, 4, 4, 5, 5, 6, 7, 7, 7, 8, 9, 10, 10, 11, 11, 12, 12, 12, 12, 13, 13, 14, 15, 15, 16, 16, 16, 16, 17, 18, 19, 19, 20, 20, 20, 21, 21, 22, 22, 22, 23, 24, 25, 25, 25, 25, 26, 26, 26, 26, 27, 27, 28, 28, 28, 28, 28, 29, 29, 30, 31, 31, 31, 31, 32

Offset: 0

Reinhard Zumkeller, Aug 23 2003

nonn

Amiram Eldar, Table of n, a(n) for n = 0..10000
Eric Weisstein's World of Mathematics, Partition Function.
Eric Weisstein's World of Mathematics, Partition Function P Congruences.

Cf. A000041, A068907, A071754, A087177, A087181, A087182, A087183.

Accumulate[Table[Boole[Mod[PartitionsP[n], 3] == 0], {n, 0, 100}]] (* Amiram Eldar, May 22 2025 *)

a(n) + A087181(n) + A087182(n) = n + 1.

A087184 Partition numbers of the form 3*k+1.

Original entry on oeis.org

1, 1, 7, 22, 385, 490, 1255, 3010, 3718, 12310, 17977, 21637, 75175, 89134, 204226, 386155, 451276, 831820, 1300156, 1741630, 5392783, 6185689, 10619863, 18004327, 20506255, 34262962, 49995925, 64112359, 104651419, 150198136

Offset: 1

Reinhard Zumkeller, Aug 23 2003

nonn

Amiram Eldar, Table of n, a(n) for n = 1..1000
Eric Weisstein's World of Mathematics, Partition Function.
Eric Weisstein's World of Mathematics, Partition Function P Congruences.

Cf. A000041, A087181, A087183, A087185, A068907, A052001, A052003, A237276.

Select[PartitionsP[Range[0, 100]], Mod[#, 3] == 1 &] (* Amiram Eldar, May 22 2025 *)

a(n) = A000041(A237276(n)). - Amiram Eldar, May 22 2025

A087185 Partition numbers of the form 3*k+2.

Original entry on oeis.org

2, 5, 11, 56, 77, 101, 176, 1958, 4565, 6842, 26015, 53174, 124754, 173525, 526823, 715220, 966467, 2012558, 2323520, 2679689, 3554345, 7089500, 9289091, 12132164, 13848650, 23338469, 26543660, 30167357, 38887673, 56634173

Offset: 1

Reinhard Zumkeller, Aug 23 2003

nonn

Harvey P. Dale, Table of n, a(n) for n = 1..1000
Eric Weisstein's World of Mathematics, Partition Function.
Eric Weisstein's World of Mathematics, Partition Function P Congruences.

Cf. A000041, A087182, A087183, A087184, A068907, A052001, A052003, A237277.

Select[PartitionsP[Range[200]],Divisible[#-2,3]&] (* Harvey P. Dale, Apr 22 2016 *)

a(n) = A000041(A237277(n)). - Amiram Eldar, May 22 2025

A127174 Numbers n of the form 3k such that partition number of n is also of the form 3k.

Original entry on oeis.org

3, 9, 21, 24, 30, 33, 39, 48, 51, 57, 63, 75, 102, 111, 129, 138, 147, 162, 180, 189, 195, 198, 207, 222, 225, 231, 240, 249, 267, 270, 288, 297, 330, 336, 339, 342, 348, 351, 354, 357, 363, 369, 372, 381, 396, 399, 402, 405, 411, 429, 432, 465, 468, 477, 480

Offset: 1

Zak Seidov, Apr 05 2007

nonn

Subset of A083214. Or, intersection of A083214 and A008585.

Cf. A000041, A008585, A083214, A087183.

with(combinat): a:=proc(k): if numbpart(3*k) mod 3 = 0 then 3*k else fi end: seq(a(n),n=1..200); # Emeric Deutsch, Apr 16 2007

Select[Range[3,600,3],Mod[PartitionsP[ # ],3]==0&]

cp's OEIS Frontend

A087180 Number partition numbers <= P(n) of the form 3*k (P = A000041).

Views

Author

Keywords

Links

Crossrefs

Programs

Mathematica

Formula

A087184 Partition numbers of the form 3*k+1.

Views

Author

Keywords

Links

Crossrefs

Programs

Mathematica

Formula

A087185 Partition numbers of the form 3*k+2.

Views

Author

Keywords

Links

Crossrefs

Programs

Mathematica

Formula

A127174 Numbers n of the form 3k such that partition number of n is also of the form 3k.

Views

Author

Keywords

Comments

Crossrefs

Programs

Maple

Mathematica

cp's OEIS Frontend

A087180 Number partition numbers <= P(n) of the form 3*k (P = A000041).

Views

Author

Keywords

Links

Crossrefs

Programs

Mathematica

Formula

A087184 Partition numbers of the form 3*k+1.

Views

Author

Keywords

Links

Crossrefs

Programs

Mathematica

Formula

A087185 Partition numbers of the form 3*k+2.

Views

Author

Keywords

Links

Crossrefs

Programs

Mathematica

Formula

A127174 Numbers n of the form 3*k such that partition number of n is also of the form 3*k.

Views

Author

Keywords

Comments

Crossrefs

Programs

Maple

Mathematica

A127174 Numbers n of the form 3k such that partition number of n is also of the form 3k.