Search: id:A121750
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%I A121750
%S A121750 0,1,5,26,184,1338,11652,108210,1140336,12849714,159858900,2117522754,
%T A121750 30442090248,463511103426,7569181895436,130254363597330,
%U A121750 2383020441932256,45738553437874962,927010880040945924
%N A121750 Number of columns of even length 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.
%C A121750 a(n)=Sum(k*A121748(n,k), k=0..n-1).
%D A121750 E. Barcucci, S. Brunetti and F. Del Ristoro, Succession rules and deco 
               polyominoes, Theoret. Informatics Appl., 34, 2000, 1-14.
%D A121750 E. Barcucci, A. Del Lungo and R. Pinzani, "Deco" polyominoes, permutations 
               and random generation, Theoretical Computer Science, 159, 1996, 29-42.
%F A121750 Recurrence relation: a(n)=n*a[n-1]+d(n-1)+(n-1)!*floor((n-1)/2) for n>
               =2, a(1)=0, where d(1)=1, d(2)=0, d(2n)=3!+5!+...+(2n-1)!, d(2n+1)=-d(2n).
%e A121750 a(2)=1 because the deco polyominoes of height 2 are the vertical and 
               horizontal dominoes, having 1 and 0 columns of even length, respectively.
%p A121750 d:=proc(n) if n=1 then 1 elif n=2 then 0 elif n mod 2 = 0 then add((2*j-1)!,
               j=2..n/2) else -d(n-1) fi end: a[1]:=0: for n from 2 to 22 do a[n]:=n*a[n-1]+d(n-1)+(n-1)!*floor((n-1)/
               2) od: seq(a[n],n=1..22);
%Y A121750 Cf. A121747, A121748.
%Y A121750 Sequence in context: A057793 A090226 A094422 this_sequence A143341 A007286 
               A099032
%Y A121750 Adjacent sequences: A121747 A121748 A121749 this_sequence A121751 A121752 
               A121753
%K A121750 nonn
%O A121750 1,3
%A A121750 Emeric Deutsch (deutsch(AT)duke.poly.edu), Aug 20 2006

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