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 A121579 Triangle read by rows: T(n,k) is the number of deco polyominoes of height n having along the lower contour exactly k reentrant corners, i.e., a vertical step that is followed by a horizontal step (n>=1, k>=0). 2
 1, 2, 5, 1, 16, 8, 65, 52, 3, 326, 344, 50, 1957, 2473, 595, 15, 13700, 19676, 6524, 420, 109601, 173472, 71862, 7840, 105, 986410, 1686912, 823836, 127232, 4410, 9864101, 17981193, 9976686, 1975750, 118125, 945, 108505112, 208769296, 128350992 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS A deco polyomino is a directed column-convex polyomino in which the height, measured along the diagonal, is attained only in the last column. Row n contains ceiling(n/2) terms. Row sums are the factorials (A000142). T(n,0) = A000522(n). T(2n+1,n) = (2n-1)!! = A001147(n) (the double factorials). Sum_{k=0..n} k*T(n,k) = A002538(n-2) for n >= 3. LINKS E. Barcucci, A. Del Lungo and R. Pinzani, "Deco" polyominoes, permutations and random generation, Theoretical Computer Science, 159, 1996, 29-42. FORMULA The row generating polynomials are P(n,t) = Q(n,t,1), where Q(1,t,x) = 1 and Q(n,t,x) = Q(n-1,t,t) + (n-1)xQ(n-1,t,1) for n >= 2. EXAMPLE T(2,0)=2 because the deco polyominoes of height 2 are the vertical and horizontal dominoes, having no reentrant corners along the lower contour. Triangle starts:     1;     2;     5,   1;    16,   8;    65,  52,   3;   326, 344,  50; MAPLE Q:=1: for n from 2 to 13 do Q[n]:=sort(expand(subs(x=t, Q[n-1])+(n-1)*x*subs(x=1, Q[n-1]))) od: for n from 1 to 13 do P[n]:=subs(x=1, Q[n]) od: for n from 1 to 13 do seq(coeff(P[n], t, j), j=0..ceil(n/2)-1) od; # yields sequence in triangular form CROSSREFS Cf. A000142, A000522, A001147, A002538. Sequence in context: A121632 A186361 A197365 * A214733 A106852 A162975 Adjacent sequences:  A121576 A121577 A121578 * A121580 A121581 A121582 KEYWORD nonn,tabf AUTHOR Emeric Deutsch, Aug 08 2006 STATUS approved

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Last modified July 28 14:19 EDT 2021. Contains 346335 sequences. (Running on oeis4.)