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A121695
Number of odd-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
1, 1, 3, 15, 57, 423, 2457, 22743, 178857, 1998423, 19774377, 259643223, 3093367977, 46722798423, 650703531177, 11118365780823, 177186743211177, 3379687537748823, 60644049519531177, 1277452054977620823
OFFSET
1,3
COMMENTS
a(n)+A121696(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-2)!(n*floor(n/2)-1) for n>=3; a(1)=a(2)=1.
Conjecture D-finite with recurrence a(n) +a(n-1) -n*(n-2)*a(n-2) -(2*n-3)*(n-2)*a(n-3) -(n-2)*(n-3)*a(n-4)=0. - R. J. Mathar, Jul 22 2022
MAPLE
a[1]:=1: a[2]:=1: for n from 3 to 23 do a[n]:=a[n-2]+(n-2)!*(n*floor(n/2)-1) od: seq(a[n], n=1..23);
CROSSREFS
Cf. A121696.
Sequence in context: A218804 A125673 A123007 * A343994 A017949 A263173
KEYWORD
nonn
AUTHOR
Emeric Deutsch, Aug 17 2006
STATUS
approved