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A119271 Triangle: number of exactly (m-1)-dimensional partitions of n, for n >= 1, m >= 0. 3

%I #26 Oct 20 2014 17:14:55

%S 1,0,1,0,1,1,0,1,3,1,0,1,5,6,1,0,1,9,18,10,1,0,1,13,44,49,15,1,0,1,20,

%T 97,172,110,21,1,0,1,28,195,512,550,216,28,1,0,1,40,377,1370,2195,

%U 1486,385,36,1,0,1,54,694,3396,7603,7886,3514,638,45,1,0,1,75,1251,7968

%N Triangle: number of exactly (m-1)-dimensional partitions of n, for n >= 1, m >= 0.

%C The partition of 1 is considered to be dimension -1 by convention.

%H Suresh Govindarajan, <a href="/A119271/b119271.txt">Rows n = 1..26 of Triangle</a>

%H Suresh Govindarajan, <a href="http://www.physics.iitm.ac.in/~suresh/partitions.html">Partitions Generator</a> (gives partitions of integers <= 25 in any dimension using this triangle).

%H Suresh Govindarajan, <a href="http://boltzmann.wikidot.com/refined-counting">Refined counting of higher-dimensional partitions</a>

%H Suresh Govindarajan, <a href="http://arxiv.org/abs/1203.4419">Notes on higher-dimensional partitions</a>, arXiv preprint arXiv:1203.4419, 2012.

%F a(n,m) = A096806(n,m-1)-a(n,m-1). Binomial transform of n-th row lists the (m-1) dimensional partitions of n.

%e Table starts:

%e 1,

%e 0,1,

%e 0,1,1,

%e 0,1,3,1,

%e 0,1,5,6,1,

%Y Cf. A119270, A096806. Column 1 is A007042.

%K nonn,tabl,hard

%O 1,9

%A _Franklin T. Adams-Watters_, May 11 2006

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Last modified March 28 05:39 EDT 2024. Contains 371235 sequences. (Running on oeis4.)