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A096004
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Number of convex triangular polyominoes containing n cells.
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0
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1, 1, 1, 2, 1, 2, 2, 3, 2, 2, 2, 3, 2, 3, 3, 5, 2, 3, 3, 4, 2, 4, 4, 6, 3, 3, 4, 5, 2, 5, 5, 7, 3, 4, 5, 6, 3, 5, 5, 8, 3, 4, 5, 6, 4, 7, 7, 9, 4, 5, 5, 7, 3, 7, 8, 9, 3, 5, 7, 8, 4, 8, 8, 11, 4, 5, 7, 8, 4, 9, 9, 11, 5, 5, 8, 9, 4, 9, 9, 13, 5, 7, 8, 9, 5, 8, 9, 12
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,4
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COMMENTS
| The main sequence on triangular polyominoes is A000577. The convexity condition makes enumeration easy as a convex triangular polyomino has at most 6 sides. It is simple to prove that a(n) is also the number of 4-tuples (p,b,c,d) of nonnegative integers satisfying b<=c<=d, b+c+d<=p, n=p^2-b^2-c^2-d^2.
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MAPLE
| a:=proc(n) local x, p, d, c, b; x:=0; for p from 0 to ceil((n+1)/2) do; for d from 0 to p do; for c from 0 to min(d, p-d) do; for b from 0 to min(c, p-c-d) do; if p^2-b^2-c^c-d^2=n then x:=x+1 fi; od; od; od; od; x; end;
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CROSSREFS
| Cf. A000577.
Sequence in context: A064122 A057526 A033265 * A193495 A071068 A137735
Adjacent sequences: A096001 A096002 A096003 * A096005 A096006 A096007
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KEYWORD
| easy,nonn
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AUTHOR
| Paul Boddington (psb(AT)maths.warwick.ac.uk), Jul 27 2004
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