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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.
2

%I #18 Nov 16 2015 05:55:25

%S 1,0,1,4,14,46,148,474,1518,4864,15590,49974,160196,513522,1646134,

%T 5276800,16915150,54222686,173814580,557174698,1786062174,5725346304,

%U 18352995094,58831800038,188589419748,604536478850,1937883656166

%N 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.

%H Dean Hickerson, <a href="http://www.cs.uwaterloo.ca/journals/JIS/HICK2/chcp.html">Counting Horizontally Convex Polyominoes</a>, J. Integer Sequences, Vol. 2 (1999), #99.1.8.

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (5,-7,4)

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

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

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

%t a[ n_ ] := a[ n ]=If[ n<6, {1, 0, 1, 4, 14}[ [ n ] ], 5a[ n-1 ]-7a[ n-2 ]+4a[ n-3 ] ]

%t LinearRecurrence[{5,-7,4},{1,0,1,4,14},40] (* _Harvey P. Dale_, Nov 16 2015 *)

%Y Cf. A049219, A049222.

%K nonn,easy

%O 1,4

%A _Dean Hickerson_, Aug 10 1999