

A006026


Number of columnconvex polyominoes with perimeter n.
(Formerly M2924)


4



1, 3, 12, 54, 260, 1310, 6821, 36413, 198227, 1096259, 6141764, 34784432, 198828308, 1145544680, 6645621536, 38786564126, 227585926704, 1341757498470, 7944249448686, 47217102715624, 281615520373954, 1684957401786580, 10110628493454482, 60830401073611514
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OFFSET

1,2


COMMENTS

With offset 2, a(n) = number of directed columnconvex polyominoes with directedsite perimeter = n. Directed means every cell (unit square) is reachable from the lower left cell, which is assumed to touch the origin. The directedsite perimeter is the number of unit squares in the first quadrant outside the polyomino but sharing at least one side with it. For example, the polyomino consisting of only one cell (with vertices (0,0),(1,0),(1,1),(0,1)) has directedsite perimeter = 2 due to the squares just above and to the right of it.  David Callan, Nov 29 2007


REFERENCES

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).


LINKS



FORMULA

The g.f. A(x) = x + x^2 + 3x^3 + ... satisfies A^3  3A^2 + (1+2x)A  x = 0.  David Callan, Nov 29 2007


MATHEMATICA

a[1]=1; a[2]=1; a[3]=3; a[n_]/; n>=4 := a[n] = ( 2(n1)(21n34)a[n1]  (3n8)(23n43)a[n2] + 16(n3)(2n7)a[n3] )/(5(n1)n); Table[a[n], {n, 10}] (* David Callan, Nov 29 2007 *)


CROSSREFS



KEYWORD

nonn,easy


AUTHOR



EXTENSIONS

Delest thesis provided by M.P. Delest and scanned by Simon Plouffe, Jan 16 2016


STATUS

approved



