A160182 Triangle read by rows, 1 / ((-1)*A129184 * A051731 + I), I = Identity matrix.

1, 1, 1, 2, 1, 1, 3, 1, 1, 1, 5, 2, 1, 1, 1, 6, 2, 1, 1, 1, 1, 10, 4, 2, 1, 1, 1, 1, 11, 4, 2, 1, 1, 1, 1, 1, 16, 6, 3, 2, 1, 1, 1, 1, 1, 19, 7, 4, 2, 1, 1, 1, 1, 1, 1, 26, 10, 5, 3, 2, 1, 1, 1, 1, 1, 1

Offset: 1

Author

Gary W. Adamson, May 03 2009

Keywords

• nonn
• tabl

Comments

Inverse mobius transform (A051731) * the triangle shifts row terms to the right deleting the right border, getting triangle A160183: (1; 2,1; 3,1,1; 5,2,1,1;...).

Examples

			First few rows of the triangle:
   1;
   1,  1;
   2,  1,  1;
   3,  1,  1,  1;
   5,  2,  1,  1,  1;
   6,  2,  1,  1,  1,  1;
  10,  4,  2,  1,  1,  1,  1;
  11,  4,  2,  1,  1,  1,  1,  1;
  16,  6,  3,  2,  1,  1,  1,  1,  1;
  19,  7,  4,  2,  1,  1,  1,  1,  1,  1;
  26, 10,  5,  3,  2,  1,  1,  1,  1,  1,  1;
  ...
		

Crossrefs

Cf. A051731, A129184, A160183.

Row sums = A068336. Left border = A003238.

Programs

Maple

A160182den := proc(n,k)
    a := add( A129184(n,i)*A051731(i,k),i=1..n) ;
    if n =k then
        -a+1 ;
    else
        -a;
    end if;
end proc:
N := 20 :
M := Matrix(N,N) :
for n from 1 to N do
for k from 1 to N do
    M[n,k] := A160182den(n,k) ;
end do:
end do:
MatrixInverse(M) ;  # R. J. Mathar, Aug 04 2015

Formula

Triangle read by rows, 1 / ((-1)*A129184 * A051731 + I), I = Identity matrix. The operations shift the inverse Mobius transform (A051731) down, changing the signs to (-1), then add I = (1,1,1,...) as the right border.