A049220 Number of horizontally convex n-ominoes in which the top row has at least 2 squares and the rightmost square in the top row is above the leftmost square in the second row.
0, 0, 1, 3, 9, 28, 89, 285, 914, 2931, 9397, 30124, 96565, 309545, 992266, 3180775, 10196193, 32684604, 104772769, 335856389, 1076610978, 3451151243, 11062904925, 35462909836, 113678819677, 364405349233, 1168126647770
Offset: 1
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.
Programs
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Mathematica
a[ n_ ] := a[ n ]=If[ n<6, {0, 0, 1, 3, 9}[ [ n ] ], 5a[ n-1 ]-7a[ n-2 ]+4a[ n-3 ] ]
Formula
G.f.: x^3 (1-x)^2/(1-5x+7x^2-4x^3).
a(n) = 5a(n-1) - 7a(n-2) + 4a(n-3) for n >= 6.
a(n) = a(n-1) + A001169(n-2) for n >= 3.