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Triangle read by rows: T(n,k) is the number of white corners of rank k in all 321-avoiding permutations of {1,2,...,n} (n>=2, 0<=k<=n-2; for definitions see the Eriksson-Linusson references).
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%I #6 Nov 28 2018 12:20:14

%S 1,3,1,9,5,2,28,19,12,5,90,68,51,33,14,297,240,197,150,98,42,1001,847,

%T 735,609,466,306,132

%N Triangle read by rows: T(n,k) is the number of white corners of rank k in all 321-avoiding permutations of {1,2,...,n} (n>=2, 0<=k<=n-2; for definitions see the Eriksson-Linusson references).

%C Sum of entries in row n is 4^(n-2) (A000302).

%C T(n,0)=A000245(n-1).

%C T(n,n-2)=Cat(n-2)=A000108(n-2).

%D K. Eriksson and S. Linusson. Combinatorics of Fulton's essential set. Duke Mathematical Journal 85(1):61-76, 1996.

%H K. Eriksson and S. Linusson, <a href="http://www.combinatorics.org/ojs/index.php/eljc/article/view/v2i1r6">The size of Fulton's essential set</a>, Electronic J. Combinatorics, Vol. 2, #R6, 1995.

%H K. Eriksson and S. Linusson, <a href="https://www.researchgate.net/publication/2550835_Combinatorics_of_Fulton&#39;s_essential_set">Combinatorics of Fulton's essential set</a>, ResearchGate, 1998.

%e Triangle starts:

%e 1;

%e 3,1;

%e 9,5,2;

%e 28,19,12,5;

%e 90,68,51,33,14;

%Y Cf. A000302, A000245, A000108, A140713.

%K nonn,tabl,more

%O 2,2

%A _Emeric Deutsch_, May 29 2008