A104726 Triangle generated as the matrix product of A026729 and A000012 (triangular views), read by rows.

1, 1, 1, 2, 2, 1, 3, 3, 3, 1, 5, 5, 5, 4, 1, 8, 8, 8, 8, 5, 1, 13, 13, 13, 13, 12, 6, 1, 21, 21, 21, 21, 21, 17, 7, 1, 34, 34, 34, 34, 34, 33, 23, 8, 1, 55, 55, 55, 55, 55, 55, 50, 30, 9, 1, 89, 89, 89, 89, 89, 89, 88, 73, 38

Offset: 0

Author

Gary W. Adamson, Mar 20 2005

Keywords

• nonn
• easy
• tabl

Comments

If the triangular factors A026729 and A000012 are commuted in the product, A004070 results.

Riordan array (1/(1-x-x^2), x*(1+x)). - Philippe Deléham, Mar 06 2013

Examples

			First few rows of the triangle are
1;
1, 1;
2, 2, 1;
3, 3, 3, 1;
5, 5, 5, 4, 1;
8, 8, 8, 8, 5, 1;
13, 13, 13, 13, 12, 6, 1;
21, 21, 21, 21, 21, 17, 7, 1;
...
Production array begins
1, 1
1, 1, 1
-1, -1, 1, 1
2, 2, -1, 1, 1
-5, -5, 2, -1, 1, 1
14, 14, -5, 2, -1, 1, 1
-42, -42, 14, -5, 2, -1, 1, 1
132, 132, -42, 14, -5, 2, -1, 1, 1
-429, -429, 132, -42, 14, -5, 2, -1, 1, 1
... which is based on A000108 or A168491. - _Philippe Deléham_, Mar 06 2013
		

Crossrefs

Cf. A001629 (row sums), A026729, A004070, A000071.

Programs

Maple

A104726 := proc(n,k)
        add( binomial(j,n-j),j=k..n) ;
end proc:
seq(seq(A104726(n,k),k=0..n),n=0..10) ; # R. J. Mathar, Oct 30 2011

Formula

T(n,k) = sum_{j=k..n} binomial(j,n-j). - R. J. Mathar, Oct 30 2011

T(n,0) = T(n-1,0) + T(n-2,0), T(n,k) = T(n-1,k-1) + T(n-2,k-1) for k>0. - Philippe Deléham, Mar 06 2013

T(2*n,n) = A000045(2n+1) = A001519(n+1) = A122367(n). - Philippe Deléham, Mar 06 2013