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A099766
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Triangle read by rows: T(n,k) = number of unbordered binary words of length n and weight k, n >= 0, 0 <= k <= n.
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1
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1, 1, 1, 0, 2, 0, 0, 2, 2, 0, 0, 2, 2, 2, 0, 0, 2, 4, 4, 2, 0, 0, 2, 4, 8, 4, 2, 0, 0, 2, 6, 12, 12, 6, 2, 0, 0, 2, 6, 18, 22, 18, 6, 2, 0, 0, 2, 8, 24, 40, 40, 24, 8, 2, 0, 0, 2, 8, 32, 60, 80, 60, 32, 8, 2, 0, 0, 2, 10, 40, 92, 140, 140, 92, 40, 10, 2, 0, 0, 2, 10, 50, 128, 232
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 0,5
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REFERENCES
| T. Harju and D. Nowotka, Counting bordered and primitive words with a fixed weight, Preprint, Oct 28, 2004. [This is the triangle U(n,k).]
T. Harju and D. Nowotka, Counting bordered and primitive words with a fixed weight, Theoret. Comput. Sci. 340 (2005), no. 2, 273-279. [This is the triangle U(n,k).]
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FORMULA
| See Maple code.
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EXAMPLE
| Triangle begins:
.1
.1,1
.0,2,0
.0,2,2,0
.0,2,2,2,0
.0,2,4,4,2,0
.0,2,4,8,4,2,0
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MAPLE
| U:=proc(n, k) option remember; if n < 1 then RETURN(0); fi; if n = 1 then RETURN(1); fi; if n > 1 and k = 0 then RETURN(0); fi; if k > 1 and k >= n then RETURN(0); fi; U(n-1, k)+U(n-1, k-1)-E(n, k); end;
E:=proc(n, k) option remember; if n mod 2 = 0 and k mod 2 = 0 then U(n/2, k/2) else 0; fi; end;
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CROSSREFS
| Row sums give A003000. Cf. A099768, A102416.
Sequence in context: A070787 A033985 A122071 * A132339 A137676 A181111
Adjacent sequences: A099763 A099764 A099765 * A099767 A099768 A099769
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KEYWORD
| nonn,tabl
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com), Nov 11 2004
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