A134311 -id:A134311 - cp's OEIS frontend

A134310 (A000012 * A134309 + A134309 * A000012) - A000012, where the sequences are interpreted as lower triangular matrices.

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, 64, 64, 65, 67, 71, 79, 95, 127, 128, 128, 129, 131, 135, 143, 159, 191, 255, 256, 256, 257, 259, 263, 271, 287, 319, 383, 511

Offset: 0

Gary W. Adamson, Oct 19 2007

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 )

			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;
  ...

Cf. A000012 (all 1's), A134309 = diag(A011782 = 2^max(n-1,0), n >= 0), A000079.

Row sums are A134311.

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

(A000012 * A134309 + A134309 * A000012) - A000012, as infinite lower triangular matrices, where A000012 = (1; 1,1; 1,1,1; ...), and A134309 = diag(1, 1, 2, 4, 8, 16, ...) = diag(A011782 = 1 followed by 1, 2, 4, 8, ... = powers of 2).

Row sums: A134311 = (1, 2, 7, 20, 51, 122, 281, 632, ...).

Edited and offset corrected to 0 by M. F. Hasler, Mar 29 2022

cp's OEIS Frontend

A134310 (A000012 * A134309 + A134309 * A000012) - A000012, where the sequences are interpreted as lower triangular matrices.

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