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A256158 Triangular array of numbers of 2-polymatroids of rank k on n labeled points, for n>=0, 0<=k<=2n. 3

%I #9 Mar 17 2015 15:53:16

%S 1,1,1,1,1,3,6,3,1,1,7,29,41,29,7,1,1,15,135,477,784,477,135,15,1,1,

%T 31,642,5957,27375,41695,27375,5957,642,31,1,1,63,3199,87477,1554077,

%U 7109189,21937982,7109189,1554077,87477,3199,63,1,1,127,16879,1604768,189213842,3559635761,733133160992,86322358307,733133160992,3559635761,189213842,1604768,16879,127,1

%N Triangular array of numbers of 2-polymatroids of rank k on n labeled points, for n>=0, 0<=k<=2n.

%C The rows are symmetric: a(n,k) = a(n,2n-k).

%C Starting with n=7, the rows are not unimodal.

%H Thomas J. Savitsky, <a href="http://epubs.siam.org/doi/abs/10.1137/140955094">Enumeration of 2-polymatroids on up to seven elements</a>. SIAM J. Discrete Math., 28(4):1641-1650, 2014. <a href="http://arxiv.org/abs/1401.8006">arXiv:1401.8006</a>

%e Triangle starts with:

%e n=0: 1

%e n=1: 1 1 1

%e n=2: 1 3 6 3 1

%e n=3: 1 7 29 41 29 7 1

%e n=4: 1 15 135 477 784 477 135 15 1

%e n=5: 1 31 642 5957 27375 41695 27375 5957 642 31 1

%e n=6: 1 63 3199 87477 1554077 7109189 21937982 7109189 1554077 87477 3199 63 1

%e n=7: 1 127 16879 1604768 189213842 3559635761 733133160992 86322358307 733133160992 3559635761 189213842 1604768 16879 127 1

%Y Cf. A256156, A256157, A256159, A058669

%K nonn,tabf

%O 0,6

%A _Max Alekseyev_, Mar 16 2015

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Last modified April 17 08:05 EDT 2024. Contains 371756 sequences. (Running on oeis4.)