A006027
Number of directed column-convex polyominoes with perimeter 2n+2.
Original entry on oeis.org
1, 1, 2, 6, 20, 71, 263, 1005, 3933, 15684, 63505, 260390, 1079019, 4511700, 19011521, 80653480, 344193353, 1476589475, 6364258163, 27545933212, 119676949397, 521739175908, 2281673067934, 10006784399183, 44002280467770, 193957104163645, 856853526774173
Offset: 1
- N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
- Alois P. Heinz, 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.
- M.-P. Delest and S. Dulucq, Enumeration of directed column-convex animals with given perimeter and area, Croat. Chem. Acta. 66 (1993), 59-80.
- E. Duchi and S. Rinaldi, An object grammar for column-convex polyominoes, Annals of Combinatorics, 8 (2004), 27-36.
- S. Dulucq, Etude combinatoire de problèmes d'énumeration, d'algorithmique sur les arbres et de codage par des mots, a thesis presented to l'Université de Bordeaux I, 1987. (Annotated scanned copy)
-
m = 30; A[_] = 0;
Do[A[x_] = (2(1-x) A[x]^2 - A[x]^3 + x^2 - x^3)/((1-x)(1-2x))+O[x]^m, {m}];
CoefficientList[1 + A[x]/x, x] (* Jean-François Alcover, Oct 05 2019 *)
A259332
Triangle read by rows: T(n,k) = number of column-convex polyominoes with perimeter n and k columns (1 <= k <= n).
Original entry on oeis.org
1, 1, 2, 1, 6, 5, 1, 12, 27, 14, 1, 20, 85, 112, 42, 1, 30, 205, 492, 450, 132, 1, 42, 420, 1582, 2565, 1782, 429, 1, 56, 770, 4172, 10415, 12562, 7007, 1430
Offset: 1
Triangle begins:
1,
1,2,
1,6,5,
1,12,27,14,
1,20,85,112,42,
1,30,205,492,450,132,
1,42,420,1582,2565,1782,429,
1,56,770,4172,10415,12562,7007,1430,
...
- 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.] See Figure 8.
- 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.
- S. Dulucq, Etude combinatoire de problèmes d'énumeration, d'algorithmique sur les arbres et de codage par des mots, a thesis presented to L'Université De Bordeaux I, 1987. (Annotated scanned copy)
A259333
Triangle read by rows: T(n,k) = number of column-convex polyominoes with bond-perimeter 2*n+2 and k columns (1 <= k <= n).
Original entry on oeis.org
1, 1, 1, 1, 4, 1, 1, 9, 9, 1, 1, 16, 37, 16, 1, 1, 25, 105, 106, 25, 1, 1, 36, 240, 446, 245, 36, 1
Offset: 1
Triangle begins:
1,
1,1,
1,4,1,
1,9,9,1,
1,16,37,16,1,
1,25,105,106,25,1,
1,36,240,446,245,36,1,
...
- 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.] See Figure 9.
- 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.
- S. Dulucq, Etude combinatoire de problèmes d'énumeration, d'algorithmique sur les arbres et de codage par des mots, a thesis presented to l'Université de Bordeaux I, 1987. (Annotated scanned copy)
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