A121752 Number of columns ending at an odd level in all deco polyominoes of height n. A deco polyomino is a directed column-convex polyomino in which the height, measured along the diagonal, is attained only in the last column.
1, 2, 7, 39, 235, 1746, 14166, 132408, 1341432, 15148080, 183764880, 2435607360, 34406268480, 523839899520, 8444375452800, 145266278169600, 2631329637350400, 50481429165619200, 1015073771517388800
Offset: 1
Keywords
Examples
a(2)=2 because the deco polyominoes of height 2 are the vertical and horizontal dominoes, having 0 and 2 columns ending at an odd level, respectively.
References
- E. Barcucci, S. Brunetti and F. Del Ristoro, Succession rules and deco polyominoes, Theoret. Informatics Appl., 34, 2000, 1-14.
- E. Barcucci, A. Del Lungo and R. Pinzani, "Deco" polyominoes, permutations and random generation, Theoretical Computer Science, 159, 1996, 29-42.
Programs
-
Maple
a[1]:=1: a[2]:=2: for n from 3 to 23 do a[n]:=(2*n-3)*a[n-1]-(n-1)*(n-3)*a[n-2]+(n-2)!*(n*floor(n/2)-(n-2)*floor((n-1)/2)-1) od: seq(a[n],n=1..23);
Formula
Recurrence relation: a(n)=(2n-3)a(n-1)-(n-1)(n-3)a(n-2)+(n-2)!(n*floor(n/2)-(n-2)*floor((n-1)/2)-1); a[1]=1, a[2]=2.
Conjecture D-finite with recurrence (-460*n+1223)*a(n) +(460*n^2+460*n-5569)*a(n-1) +(460*n^3-3826*n^2+7853*n+1313)*a(n-2) +(-460*n^4+1840*n^3+5501*n^2-31045*n+31726)*a(n-3) +(1223*n^4-13205*n^3+45787*n^2-51389*n+558)*a(n-4) -2*(426*n-1111)*(n-6)*(n-4)^2*a(n-5)=0. - R. J. Mathar, Jul 26 2022
Comments