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A121580
Number of cells in column 1 of 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.
2
1, 3, 11, 53, 317, 2237, 18077, 164237, 1656077, 18348557, 221561357, 2895986957, 40737113357, 613623026957, 9854521894157, 168083120422157, 3034505335078157, 57810369261862157, 1159018646647078157
OFFSET
1,2
LINKS
E. Barcucci, A. Del Lungo and R. Pinzani,"Deco" polyominoes, permutations and random generation,Theoretical Computer Science, 159, 1996, 29-42.
FORMULA
a(1) = 1, a(n) = a(n-1)+(n-1)!*(1+n*(n-1)/2) for n>=2.
a(n) = Sum_{k=1..n} k*A100822(n,k).
a(n) = (1/2)*Sum_{j=0..n+1} j! - n!. -Emeric Deutsch,Apr 06 2008
Conjecture D-finite with recurrence a(n) +(-n-4)*a(n-1) +3*(n+1)*a(n-2) +2*(-2*n+3)*a(n-3) +2*(n-3)*a(n-4)=0. -R. J. Mathar,Jul 26 2022
EXAMPLE
a(2)=3 because the deco polyominoes of height 2 are the vertical and horizontal dominoes, having, respectively, 2 and 1 cells in their first columns.
MAPLE
a[1]:=1: for n from 2 to 22 do a[n]:=a[n-1]+(n-1)!*(1+n*(n-1)/2) od: seq(a[n], n=1..22);
KEYWORD
nonn,easy
AUTHOR
Emeric Deutsch,Aug 09 2006
STATUS
approved