A049219 Number of horizontally convex n-ominoes in which the top row has exactly 1 square.

1, 1, 3, 10, 33, 107, 344, 1103, 3535, 11330, 36317, 116415, 373176, 1196243, 3834643, 12292218, 39403561, 126310851, 404898200, 1297929287, 4160602439, 13337099986, 42753000005, 137047709879, 439315949304, 1408257777387

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. A001169, A049221.

Programs

Mathematica

a[ n_ ] := a[ n ]=If[ n<5, {1, 1, 3, 10}[ [ n ] ], 5a[ n-1 ]-7a[ n-2 ]+4a[ n-3 ] ]
LinearRecurrence[{5,-7,4},{1,1,3,10,33,107},40] (* Harvey P. Dale, Nov 19 2019 *)

Formula

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

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

a(n) = A001169(n-1) + A049221(n) for n >= 2.