login
This site is supported by donations to The OEIS Foundation.

 

Logo

Please make a donation to keep the OEIS running. We are now in our 55th year. In the past year we added 12000 new sequences and reached 8000 citations (which often say "discovered thanks to the OEIS"). We need to raise money to hire someone to manage submissions, which would reduce the load on our editors and speed up editing.
Other ways to donate

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A089299 Number of square plane partitions of n. 13
1, 1, 1, 1, 2, 2, 4, 5, 8, 11, 16, 21, 31, 41, 57, 78, 108, 146, 202, 274, 375, 509, 690, 929, 1255, 1679, 2246, 2991, 3979, 5266, 6971, 9187, 12104, 15898, 20870, 27322, 35762, 46690, 60927, 79348, 103270, 134138, 174108, 225576, 291990, 377320, 487083 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,5

COMMENTS

Number of ways of writing n as a sum p(1,1) + p(1,2) + ... + p(1,k) + p(2,1) + ... + p(2,k) + ... + p(k,1) + ... + p(k,k) for some k so that in the square array {p(i,j)} the numbers are nonincreasing along rows and columns. All the p(i,j) are >= 1.

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..4000

FORMULA

G.f.: Sum_{k>=0} x^(k^2) / Product_{j=1..2k-1} (1-x^j)^min(j,2k-j). - Franklin T. Adams-Watters, Jun 14 2006

EXAMPLE

a(7) = 5:

7 41 32 31 22

. 11 11 21 21

a(10) = 16 from {{10}}, {{3, 2}, {3, 2}}, {{3, 3}, {2, 2}}, {{3, 3}, {3, 1}}, {{4, 1}, {4, 1}}, {{4, 2}, {2, 2}}, {{4, 2}, {3, 1}}, {{4, 3}, {2, 1}}, {{4, 4}, {1, 1}}, {{5, 1}, {3, 1}}, {{5, 2}, {2, 1}}, {{5, 3}, {1, 1}}, {{6, 1}, {2, 1}}, {{6, 2}, {1, 1}}, {{7, 1}, {1, 1}}, {{2, 1, 1}, {1, 1, 1}, {1, 1, 1}}}

From Gus Wiseman, Jan 16 2019: (Start)

The a(10) = 16 square plane partitions:

  [ten]

.

  [32] [33] [33] [41] [42] [42] [43] [44] [51] [52] [53] [61] [62] [71]

  [32] [22] [31] [41] [22] [31] [21] [11] [31] [21] [11] [21] [11] [11]

.

  [211]

  [111]

  [111]

(End)

MATHEMATICA

Table[Sum[Length[Select[Union[Sort/@Tuples[IntegerPartitions[#, {Length[ptn]}]&/@ptn]], And@@OrderedQ/@Transpose[#]&]], {ptn, IntegerPartitions[n]}], {n, 30}] (* Gus Wiseman, Jan 16 2019 *)

CROSSREFS

Cf. A008763, A001970, A089292.

Cf. A000219, A003293, A101509, A319066, A323429, A323433, A323450.

Sequence in context: A241545 A157162 A109434 * A017910 A240734 A328460

Adjacent sequences:  A089296 A089297 A089298 * A089300 A089301 A089302

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Dec 25 2003

EXTENSIONS

Corrected and extended by Wouter Meeussen, Dec 30 2003

a(21)-a(25) from John W. Layman, Jan 02 2004

More terms from Franklin T. Adams-Watters, Jun 14 2006

Name edited by Gus Wiseman, Jan 16 2019

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified December 8 14:38 EST 2019. Contains 329865 sequences. (Running on oeis4.)