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

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A089292 G.f.: Product_{m>=1} 1/(1-x^m)^A018819(m). 5
1, 1, 3, 5, 12, 20, 41, 69, 132, 222, 399, 665, 1156, 1904, 3212, 5234, 8645, 13925, 22596, 36008, 57590, 90862, 143508, 224316, 350505, 543159, 840623, 1292317, 1983094, 3026178, 4608061, 6983663, 10559800, 15901698, 23889722, 35760786, 53405395, 79498207 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Number of 2-dimensional partitions of n where each row is non-squashing.

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..5000

N. J. A. Sloane and J. A. Sellers, On non-squashing partitions, arXiv:math/0312418 [math.CO], 2003.

N. J. A. Sloane and J. A. Sellers, On non-squashing partitions, Discrete Math., 294 (2005), 259-274.

EXAMPLE

a(4) = 12:

4.31.3.22.2.211.21.2..2.11.11.1

.....1....2.....1..11.1.11.1..1

......................1....1..1

..............................1

211 and 1111 for example are excluded because they would squash.

MATHEMATICA

maxm = 38;

b[0] = b[1] = 1; b[n_] := b[n] = If[OddQ[n], b[n-1], b[n-1] + b[n/2]];

Product[1/(1-x^m)^b[m], {m, 1, maxm}] + O[x]^maxm // CoefficientList[#, x]&

(* Jean-Fran├žois Alcover, Oct 02 2018 *)

CROSSREFS

Cf. A000123, A018819, A001970.

Sequence in context: A321679 A266819 A245939 * A309702 A143360 A234005

Adjacent sequences:  A089289 A089290 A089291 * A089293 A089294 A089295

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Dec 24 2003

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 September 21 13:37 EDT 2019. Contains 327253 sequences. (Running on oeis4.)