OFFSET
0,4
COMMENTS
From M. F. Hasler, Mar 29 2022: (Start)
Both A000012 and A134309 have offset 0, so this triangular matrix also has row and column indices starting at 0.
Right (resp. left) multiplication by a diagonal matrix (such as A134309) amounts to multiplying the columns (resp. rows) of the other matrix by the diagonal elements. Therefore this matrix is the sum of the two lower triangular matrices with columns (resp. rows) filled with the same element given by sequence A134309 = (1, 1, 2, 4, 8, 16, ...), i. e., restricted to upper left 5 X 5 square:
( 1 ) ( 1 ) ( 1 )
( 1 1 ) ( 1 1 ) ( 1 1 )
(this) = ( 1 1 2 ) + ( 2 2 2 ) - ( 1 1 1 ) . (End)
( 1 1 2 4 ) ( 4 4 4 4 ) ( 1 1 1 1 )
( 1 1 2 4 8 ) ( 8 8 8 8 8 ) ( 1 1 1 1 1 )
FORMULA
EXAMPLE
First few rows of the triangle:
1;
1, 1;
2, 2, 3;
4, 4, 5, 7;
8, 8, 9, 11, 15;
16, 16, 17, 19, 23, 31;
32, 32, 33, 35, 39, 47, 63;
...
PROG
(PARI) A134310(r, c)=if(r>=c, 2^max(c-1, 0)+2^max(r-1, 0)-1)
matrix(8, 8, i, j, A134310(i-1, j-1)) \\ M. F. Hasler, Mar 29 2022
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Gary W. Adamson, Oct 19 2007
EXTENSIONS
Edited and offset corrected to 0 by M. F. Hasler, Mar 29 2022
STATUS
approved