|
Search: id:A140710
|
|
|
| A140710 |
|
Number of maximal initial consecutive columns ending at the same level, summed over 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). |
|
+0
2
|
|
| 1, 3, 10, 38, 172, 944, 6208, 47696, 417952, 4101824, 44491648, 528068096, 6804155392, 94559581184, 1409615239168, 22434345998336, 379633330204672, 6805952938041344, 128854632579186688, 2568966172926181376
(list; graph; listen)
|
|
|
OFFSET
|
1,2
|
|
|
COMMENT
|
a(n)=Sum(k*A140709(n,k),k=1..n).
|
|
REFERENCES
|
E. Barcucci, A. del Lungo and R. Pinzani, "Deco" polyominoes, permutations and random generation, Theoretical Computer Science, 159, 1996, 29-42.
|
|
FORMULA
|
a(n)=2^(n-1)*[1+sum(j^2*(j-1)!/2^j,j=1..n-1)] (n>=1). Rec. rel.: a(n)=(n-1)!(n-1) + 2a(n-1); a(1)=1.
|
|
EXAMPLE
|
a(3)=10 because the 6 deco polyominoes of height 3 have columns ending at levels 3, 22, 12, 111, 22, 122, respectively and 1+2+1+3+2+1=10.
|
|
MAPLE
|
a:=proc(n) options operator, arrow: 2^(n-1)*(1+sum(j^2*factorial(j-1)/2^j, j= 1..n-1)) end proc: seq(a(n), n=1..20);
|
|
CROSSREFS
|
Cf. A140709.
Sequence in context: A103138 A074527 A010842 this_sequence A103296 A111749 A149048
Adjacent sequences: A140707 A140708 A140709 this_sequence A140711 A140712 A140713
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
Emeric Deutsch (deutsch(AT)duke.poly.edu), Jun 03 2008
|
|
|
Search completed in 0.002 seconds
|
