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

0,6

Comments

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

Links

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

Formula

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

Example

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;

Mathematica

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 *)

Crossrefs

Cf. A084938, A085791.

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

Sequence in context: A201910 A109450 A086810 * A094456 A010028 A151860

Adjacent sequences: A085835 A085836 A085837 * A085839 A085840 A085841

Keyword

nonn,tabl

Author

N. J. A. Sloane, Aug 16 2003

Status

approved