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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.
2
1, 2, 7, 39, 235, 1746, 14166, 132408, 1341432, 15148080, 183764880, 2435607360, 34406268480, 523839899520, 8444375452800, 145266278169600, 2631329637350400, 50481429165619200, 1015073771517388800
OFFSET
1,2
COMMENTS
a(n)=Sum(k*A121697(n,k),k=0..n).
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.
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
EXAMPLE
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.
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);
CROSSREFS
Sequence in context: A337685 A014058 A119602 * A054133 A330470 A364336
KEYWORD
nonn
AUTHOR
Emeric Deutsch, Aug 23 2006
STATUS
approved