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

1,4

Links

Table of n, a(n) for n=1..27.

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)

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.

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 *)

Crossrefs

Cf. A049219, A049222.

Sequence in context: A026290 A027649 A330796 * A081670 A297016 A258255

Adjacent sequences: A049218 A049219 A049220 * A049222 A049223 A049224

Keyword

nonn,easy

Author

Dean Hickerson, Aug 10 1999

Status

approved