A049219 - OEIS

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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

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,3

LINKS

Table of n, a(n) for n=1..26.

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 (1-2x)/(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.

MATHEMATICA