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A121693 Number of deco polyominoes of height n and vertical height 3 (i.e., having 3 rows). 1
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,4
COMMENTS
A deco polyomino is a directed column-convex polyomino in which the height, measured along the diagonal, is attained only in the last column.
LINKS
E. Barcucci, S. Brunetti and F. Del Ristoro, Succession rules and deco polyominoes, Theoret. Informatics Appl., 34, 2000, 1-14.
E. Barcucci, A. Del Lungo and R. Pinzani, "Deco" polyominoes, permutations and random generation, Theoretical Computer Science, 159, 1996, 29-42.
FORMULA
a(n) = A121692(n,3).
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)).
MAPLE
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);
CROSSREFS
Cf. A121692.
Sequence in context: A071270 A051877 A212065 * A190297 A072259 A272233
KEYWORD
nonn,easy
AUTHOR
Emeric Deutsch, Aug 17 2006
STATUS
approved

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Last modified February 21 13:52 EST 2024. Contains 370235 sequences. (Running on oeis4.)