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%I #20 Jul 31 2015 11:12:22
%S 0,0,0,1,4,13,41,130,415,1329,4260,13657,43781,140346,449891,1442157,
%T 4622932,14819125,47503729,152276498,488132887,1564743865,5015895108,
%U 16078800033,51541709869,165220529546,529625878779,1697752526549
%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 and the rightmost square in the second row is above the leftmost square in the third 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^4 (1-x)/(1-5x+7x^2-4x^3).
%F a(n) = 5*a(n-1) - 7*a(n-2) + 4*a(n-3) for n >= 6.
%F a(n) = a(n-1) + A049220(n-1) for n >= 2.
%t a[ n_ ] := a[ n ]=If[ n<6, {0, 0, 0, 1, 4}[ [ n ] ], 5a[ n-1 ]-7a[ n-2 ]+4a[ n-3 ] ]
%t Join[{0,0,0},LinearRecurrence[{5,-7,4},{0,1,4},30]] (* or *) CoefficientList[ Series[x^4 (1-x)/(1-5x+7x^2-4x^3),{x,0,30}],x] (* _Harvey P. Dale_, May 10 2011 *)
%Y Cf. A049220.
%K nonn,easy
%O 1,5
%A _Dean Hickerson_, Aug 10 1999
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