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Triangle of numbers a(n,k) = number of permutations on n letters containing k 3-sequences (n >= 0, 0<=k<=max(0,n-2)).
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%I #15 Apr 20 2021 17:06:00

%S 1,1,2,5,1,21,2,1,106,11,2,1,643,62,12,2,1,4547,406,71,13,2,1,36696,

%T 3046,481,80,14,2,1,332769,25737,3708,559,89,15,2,1,3349507,242094,

%U 32028,4414,640,98,16,2,1,37054436,2510733,306723,38893,5164,724,107,17,2,1

%N Triangle of numbers a(n,k) = number of permutations on n letters containing k 3-sequences (n >= 0, 0<=k<=max(0,n-2)).

%H J. Riordan, <a href="http://projecteuclid.org/euclid.bams/1183507357">Permutations without 3-sequences</a>, Bull. Amer. Math. Soc., 51 (1945), 745-748.

%F Riordan gives a recurrence.

%e Triangle begins:

%e 1;

%e 1;

%e 2;

%e 5, 1;

%e 21, 2, 1;

%e 106, 11, 2, 1;

%e 643, 62, 12, 2, 1;

%e 4547, 406, 71, 13, 2, 1;

%e 36696, 3046, 481, 80, 14, 2, 1;

%e 332769, 25737, 3708, 559, 89, 15, 2, 1;

%e ...

%Y Columns give A002628, A002629, A002630.

%Y Row sums give A000142.

%K nonn,tabf,nice,easy

%O 0,3

%A _N. J. A. Sloane_

%E Edited and extended by _Max Alekseyev_, Sep 05 2010

%E a(0,0) = a(1,0) = 1 prepended by _Alois P. Heinz_, Apr 20 2021