A059682 Triangle T(n,k) giving number of 2 X k polyominoes with n cells (n >= 2, 1<=k<=n-1).

1, 0, 1, 0, 1, 3, 0, 0, 2, 3, 0, 0, 1, 6, 5, 0, 0, 0, 2, 11, 5, 0, 0, 0, 1, 10, 19, 7, 0, 0, 0, 0, 3, 22, 28, 7, 0, 0, 0, 0, 1, 15, 52, 40, 9, 0, 0, 0, 0, 0, 3, 45, 90, 53, 9, 0, 0, 0, 0, 0, 1, 21, 119, 158, 69, 11, 0, 0, 0, 0, 0, 0, 4, 73, 257, 238, 86, 11, 0, 0, 0, 0, 0, 0, 1, 28, 237, 505, 360, 106, 13

Offset: 2

Author

N. J. A. Sloane, Feb 05 2001

Keywords

• nonn
• easy
• nice
• tabl

Examples

			Triangle starts:
1;
0,1;
0,1,3;
0,0,2,3;
...
		

Links

• R. C. Read, Contributions to the cell growth problem, Canad. J. Math., 14 (1962), 1-20. See Eq. (8.5) for g.f..

Crossrefs

Main diagonal gives A109613(n-2).

Cf. A059683 (3xk), A059684 (4xk).

Programs

Mathematica

rows = 13; gf = ((y^9 - y^8)*x^6 + y^8*x^5 + (y^7 - 2*y^6 + y^5)*x^4 + (y^6 - y^3)*x^3 + (-y^4 + y^2)*x^2 + (-y^2 - y)*x + 1)*y^2*x/((y^3*x^2 + (y^2 + y)*x - 1)*(y*x - 1)*(y^2*x - 1)*(y^6*x^4 + (y^4 + y^2)*x^2 - 1));
coes = CoefficientList[#, x]& /@ CoefficientList[gf + O[y]^(rows+2), y];
T[n_, k_] := coes[[n+1, k+1]];
Table[T[n, k], {n, 2, rows+1}, {k, 1, n-1}] // Flatten (* Jean-François Alcover, Nov 12 2017, after Vladeta Jovovic *)

Formula

G.f.: ((y^9-y^8)*x^6+y^8*x^5+(y^7-2*y^6+y^5)*x^4+(y^6-y^3)*x^3+(-y^4+y^2)*x^2+(-y^2-y)*x+1)*y^2*x/((y^3*x^2+(y^2+y)*x-1)*(y*x-1)*(y^2*x-1)*(y^6*x^4+(y^4+y^2)*x^2-1)). - Vladeta Jovovic, Apr 02 2002

Extensions

More terms from Vladeta Jovovic, Apr 02 2002