A049221 Number of horizontally convex n-ominoes in which the top row has exactly 1 square, which is not above the rightmost square in the second row.

1, 0, 1, 4, 14, 46, 148, 474, 1518, 4864, 15590, 49974, 160196, 513522, 1646134, 5276800, 16915150, 54222686, 173814580, 557174698, 1786062174, 5725346304, 18352995094, 58831800038, 188589419748, 604536478850, 1937883656166

Offset: 1

Author

Dean Hickerson, Aug 10 1999

Keywords

• nonn
• easy

Links

• Dean Hickerson, Counting Horizontally Convex Polyominoes, J. Integer Sequences, Vol. 2 (1999), #99.1.8.
• Index entries for linear recurrences with constant coefficients, signature (5,-7,4)

Crossrefs

Cf. A049219, A049222.

Programs

Mathematica

a[ n_ ] := a[ n ]=If[ n<6, {1, 0, 1, 4, 14}[ [ n ] ], 5a[ n-1 ]-7a[ n-2 ]+4a[ n-3 ] ]
LinearRecurrence[{5,-7,4},{1,0,1,4,14},40] (* Harvey P. Dale, Nov 16 2015 *)

Formula

G.f.: x (1-x)^2 (1-3x+x^2)/(1-5x+7x^2-4x^3).

a(n) = 5a(n-1) - 7a(n-2) + 4a(n-3) for n >= 6.

a(n) = A049219(n-1) + A049222(n) for n >= 3.