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

1,4

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;...).

Links

Table of n, a(n) for n=1..66.

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.

Example

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;
  ...

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

Crossrefs

Cf. A051731, A129184, A160183.

Row sums = A068336. Left border = A003238.

Sequence in context: A124021 A109626 A182285 * A195825 A098824 A181651

Adjacent sequences: A160179 A160180 A160181 * A160183 A160184 A160185

Keyword

nonn,tabl

Author

Gary W. Adamson, May 03 2009

Status

approved