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A160182 Triangle read by rows, 1 / ((-1)*A129184 * A051731 + I), I = Identity matrix. 2
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 (list; table; graph; refs; listen; history; text; internal format)
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

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Last modified May 18 04:22 EDT 2021. Contains 343994 sequences. (Running on oeis4.)