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

0,4

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

Links

Table of n, a(n) for n=0..63.

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

Example

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

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

Crossrefs

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

Sequence in context: A294453 A097094 A210870 * A364954 A194195 A164999

Adjacent sequences: A104723 A104724 A104725 * A104727 A104728 A104729

Keyword

nonn,easy,tabl

Author

Gary W. Adamson, Mar 20 2005

Status

approved