OFFSET
1,3
COMMENTS
a(n)=A121697(n,0).
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)=2floor((n-1)/2)a(n-1)-[floor((n-1)/2)floor((n-2)/2)-1]a(n-2) for n>=3, a(1)=0, a(2)=1.
Conjecture D-finite with recurrence +256*a(n) -384*a(n-1) +16*(-8*n^2+40*n-67)*a(n-2) +16*(8*n^2-54*n+87)*a(n-3) +4*(4*n^4-56*n^3+242*n^2-304*n-21)*a(n-4) +4*(-2*n^4+38*n^3-249*n^2+647*n-554)*a(n-5) +(n-4)*(n-8)*(n^2-12*n+31)*a(n-6)=0. - R. J. Mathar, Jul 26 2022
EXAMPLE
a(2)=1 because the deco polyominoes of height 2 are the vertical and horizontal dominoes and only the vertical one has all of its columns ending at an even level.
MAPLE
a[1]:=0: a[2]:=1: for n from 3 to 26 do a[n]:=2*floor((n-1)/2)*a[n-1]-(floor((n-1)/2)*floor((n-2)/2)-1)*a[n-2] od: seq(a[n], n=1..26);
CROSSREFS
KEYWORD
nonn
AUTHOR
Emeric Deutsch, Aug 23 2006
STATUS
approved