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A121693
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Number of deco polyominoes of height n and vertical height 3 (i.e., having 3 rows).
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1
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0, 0, 1, 12, 57, 216, 741, 2412, 7617, 23616, 72381, 220212, 666777, 2012616, 6062421, 18236412, 54807537, 164619216, 494250861, 1483539012, 4452189897, 13359715416, 40085437701, 120268896012, 360831853857, 1082545893216
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OFFSET
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1,4
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COMMENTS
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A deco polyomino is a directed column-convex polyomino in which the height, measured along the diagonal, is attained only in the last column.
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LINKS
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FORMULA
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a(n) = 23*3^(n-3)/2 + 3/2 - 3*2^(n-1) for n >= 3.
Recurrence relation: a(n) = 3(a(n-1) + 2^(n-2) - 1) for n >= 4, a(1) = a(2) = 0, a(3) = 1.
G.f. = x^3*(1+6x-4x^2)/((1-x)(1-2x)(1-3x)).
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MAPLE
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a[1]:=0: a[2]:=0: a[3]:=1: for n from 4 to 30 do a[n]:=3*(a[n-1]+2^(n-2)-1) od: seq(a[n], n=1..30);
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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