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, 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

Offset

0,5

Links

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

T. Harju and D. Nowotka, Counting bordered and primitive words with a fixed weight, TUCS Technical Report, No 630, Turku, November 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).]

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: A122071 A353724 A326915 * A194947 A132339 A333941

Adjacent sequences: A099763 A099764 A099765 * A099767 A099768 A099769

Keyword

nonn,tabl

Author

N. J. A. Sloane, Nov 11 2004

Status

approved