login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A236406 Triangle read by rows: number of (1-2-3)-avoiding permutations on n letters with k peaks. 2
1, 1, 2, 3, 2, 4, 10, 5, 32, 5, 6, 84, 42, 7, 198, 210, 14, 8, 438, 816, 168, 9, 932, 2727, 1152, 42, 10, 1936, 8250, 5940, 660, 11, 3962, 23276, 25630, 5775, 132, 12, 8034, 62400, 97812, 37180, 2574, 13, 16200, 160953, 341224, 196625, 27456, 429, 14, 32556, 402906, 1111656, 905086, 212212, 10010 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,3
COMMENTS
This is a convolution of A091156 with itself (see the Pudwell link below).
LINKS
A. M. Baxter, Refining enumeration schemes to count according to permutation statistics, arXiv preprint arXiv:1401.0337 [math.CO], 2014.
M. Bukata, R. Kulwicki, N. Lewandowski, L. Pudwell, J. Roth, and T. Wheeland, Distributions of Statistics over Pattern-Avoiding Permutations, arXiv preprint arXiv:1812.07112 [math.CO], 2018.
FORMULA
T(2*n+2,n) = A276666(n+2) = (n+1)*A000108(n+2). - Alois P. Heinz, Apr 27 2018
G.f.: G(q,z) = - (-2z^3q^2+4z^3q-2z^3-2z^2q+2z^2-1+sqrt(-4z^2q+4z^2-4z+1))/(2z(zq-z+1)^2). (See the Pudwell link above.)
EXAMPLE
Triangle begins:
1;
1;
2;
3, 2;
4, 10;
5, 32, 5;
6, 84, 42;
7, 198, 210, 14;
8, 438, 816, 168;
9, 932, 2727, 1152, 42;
10, 1936, 8250, 5940, 660;
...
MATHEMATICA
m = maxExponent = 15;
G = -(-2 z^3 q^2 + 4z^3 q - 2z^3 - 2z^2 q + 2z^2 - 1 + Sqrt[-4z^2 q + 4z^2 - 4z + 1])/(2z (z q - z + 1)^2);
CoefficientList[# + O[q]^m, q]& /@ CoefficientList[G + O[z]^m, z]// Flatten (* Jean-François Alcover, Aug 06 2018 *)
CROSSREFS
Row sums give A000108.
Sequence in context: A034800 A082771 A127157 * A247497 A202714 A022662
KEYWORD
nonn,tabf
AUTHOR
N. J. A. Sloane, Jan 31 2014
EXTENSIONS
More terms from Alois P. Heinz, Apr 26 2018
STATUS
approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified July 17 08:16 EDT 2024. Contains 374360 sequences. (Running on oeis4.)