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A099766 Triangle read by rows: T(n,k) = number of unbordered binary words of length n and weight k, n >= 0, 0 <= k <= n. 1
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; text; internal format)
OFFSET

0,5

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).]

LINKS

Table of n, a(n) for n=0..83.

FORMULA

See Maple code.

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

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;

CROSSREFS

Row sums give A003000. Cf. A099768, A102416.

Sequence in context: A033985 A216218 A122071 * A194947 A132339 A137676

Adjacent sequences:  A099763 A099764 A099765 * A099767 A099768 A099769

KEYWORD

nonn,tabl

AUTHOR

N. J. A. Sloane, Nov 11 2004

STATUS

approved

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Last modified August 24 02:32 EDT 2019. Contains 326260 sequences. (Running on oeis4.)