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A121696
Number of even-length first columns 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
0, 1, 3, 9, 63, 297, 2583, 17577, 184023, 1630377, 20142423, 219358377, 3133652823, 40455492777, 656970836823, 9804424107177, 178500684884823, 3022686167979177, 61001050889300823, 1155449953199019177
OFFSET
1,3
COMMENTS
a(n)+A121695(n)=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
a(n)=a(n-2)+n(n-2)!*floor((n-1)/2) for n>=3; a(1)=0, a(2)=1.
Conjecture D-finite with recurrence a(n) -(n-1)^2*a(n-2) -n*(n-2)*a(n-3)=0. - R. J. Mathar, Jul 22 2022
MAPLE
a[1]:=0: a[2]:=1: for n from 3 to 23 do a[n]:=a[n-2]+n*(n-2)!*floor((n-1)/2) od: seq(a[n], n=1..23);
CROSSREFS
Cf. A121695.
Sequence in context: A269961 A064703 A085435 * A108557 A109285 A245165
KEYWORD
nonn
AUTHOR
Emeric Deutsch, Aug 17 2006
STATUS
approved