This site is supported by donations to The OEIS Foundation.

 Please make a donation to keep the OEIS running. We are now in our 55th year. In the past year we added 12000 new sequences and reached 8000 citations (which often say "discovered thanks to the OEIS"). We need to raise money to hire someone to manage submissions, which would reduce the load on our editors and speed up editing. Other ways to donate

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A006026 Number of column-convex 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS With offset 2, a(n) = number of directed column-convex polyominoes with directed-site perimeter = n. Directed means every cell (unit square) is reachable from the lower left cell, which is assumed to touch the origin. The directed-site 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 directed-site 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 Colin Barker, Table of n, a(n) for n = 1..1000 M.-P. Delest, Utilisation des Langages Algébriques et du Calcul Formel Pour le Codage et l'Enumeration des Polyominos, Ph.D. Dissertation, Université Bordeaux I, May 1987. [Scanned copy, with permission. A very large file.] M.-P. Delest, Utilisation des Langages Algébriques et du Calcul Formel Pour le Codage et l'Enumeration des Polyominos, Ph.D. Dissertation, Université Bordeaux I, May 1987. (Annotated scanned copy of a small part of the thesis) M.-P. Delest, Generating functions for column-convex polyominoes, J. Combin. Theory Ser. A 48 (1988), no. 1, 12-31. G. S. Joyce and A. J. Guttmann, Exact results for the generating function of directed column-convex animals on the square lattice, J. Physics A: Math. General 27 (1994) 4359-4367. 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(n-1)(21n-34)a[n-1] - (3n-8)(23n-43)a[n-2] + 16(n-3)(2n-7)a[n-3] )/(5(n-1)n); Table[a[n], {n, 10}] (* David Callan, Nov 29 2007 *) CROSSREFS Sequence in context: A055835 A125188 A054666 * A158826 A107264 A200740 Adjacent sequences:  A006023 A006024 A006025 * A006027 A006028 A006029 KEYWORD nonn,easy AUTHOR EXTENSIONS Delest thesis provided by M.=P. Delest and scanned by Simon Plouffe, Jan 16 2016 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified December 11 23:44 EST 2019. Contains 329945 sequences. (Running on oeis4.)