A085791 -id:A085791 - cp's OEIS frontend

A085838 Triangle T(n,k) read by rows; given by [0,1,0,1,0,1,0,1,...] DELTA [1,1,1,2,1,3,1,4,1,5,1,6,...], where DELTA is Deléham's operator defined in A084938.

1, 0, 1, 0, 1, 2, 0, 1, 5, 5, 0, 1, 9, 22, 15, 0, 1, 14, 60, 98, 52, 0, 1, 20, 130, 366, 457, 203, 0, 1, 27, 245, 1031, 2190, 2254, 877, 0, 1, 35, 420, 2436, 7652, 13251, 11788, 4140, 0, 1, 44, 672, 5096, 21862, 55499, 82288, 65330, 21147, 0, 1, 54, 1020, 9744, 54216, 186595, 402582, 528400, 382948, 115975

Offset: 0

N. J. A. Sloane, Aug 16 2003

T(n,k) appears to be the number of indecomposable permutations of [n+1] that avoid both of the dashed patterns 41-32 and 32-41 and contain n+1-k right-to-left minima. For example, T(3,1)=1 counts 4123 with 3 right-to-left minima; T(3,2)=5 counts 2413, 3142, 3412, 4213, 4312, each with 2 right-to-left minima; and T(3,3)=5 counts 2341, 2431, 3421, 4231, 4321, each with 1 right-to-left minimum. - David Callan, Aug 27 2014

			1;
0, 1;
0, 1,  2;
0, 1,  5,  5;
0, 1,  9,  22,   15;
0, 1, 14,  60,   98,   52;
0, 1, 20, 130,  366,  457,   203;
0, 1, 27, 245, 1031, 2190,  2254,   877;
0, 1, 35, 420, 2436, 7652, 13251, 11788, 4140;

Alois P. Heinz, Rows n = 0..140, flattened

Cf. A084938, A085791.

Diagonals : A000007, A000012, A000096, A000110. Row sums : A090365

m = 13;
(* DELTA is defined in A084938 *)
DELTA[Table[{0, 1}, {m/2 // Ceiling}] // Flatten, LinearRecurrence[{0, 2, 0, -1}, {1, 1, 1, 2}, m], m] // Flatten (* Jean-François Alcover, Feb 19 2020 *)

Sum_{k=0..n} (-x)^(n-k)*T(n,k) = A090365(n), A000110(n), A000012(n), A010892(n) for x=-1, 0, 1, 2. - Philippe Deléham, Oct 26 2006

cp's OEIS Frontend

A085838 Triangle T(n,k) read by rows; given by [0,1,0,1,0,1,0,1,...] DELTA [1,1,1,2,1,3,1,4,1,5,1,6,...], where DELTA is Deléham's operator defined in A084938.

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