A160182 - OEIS

%I #14 Mar 05 2019 02:17:45

%S 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,

%T 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

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

%C 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;...).

%F 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.

%e First few rows of the triangle:

%e    1;

%e    1,  1;

%e    2,  1,  1;

%e    3,  1,  1,  1;

%e    5,  2,  1,  1,  1;

%e    6,  2,  1,  1,  1,  1;

%e   10,  4,  2,  1,  1,  1,  1;

%e   11,  4,  2,  1,  1,  1,  1,  1;

%e   16,  6,  3,  2,  1,  1,  1,  1,  1;

%e   19,  7,  4,  2,  1,  1,  1,  1,  1,  1;

%e   26, 10,  5,  3,  2,  1,  1,  1,  1,  1,  1;

%e   ...

%p A160182den := proc(n,k)

%p     a := add( A129184(n,i)*A051731(i,k),i=1..n) ;

%p     if n =k then

%p         -a+1 ;

%p     else

%p         -a;

%p     end if;

%p end proc:

%p N := 20 :

%p M := Matrix(N,N) :

%p for n from 1 to N do

%p for k from 1 to N do

%p     M[n,k] := A160182den(n,k) ;

%p end do:

%p end do:

%p MatrixInverse(M) ;  # _R. J. Mathar_, Aug 04 2015

%Y Cf. A051731, A129184, A160183.

%Y Row sums = A068336. Left border = A003238.

%K nonn,tabl

%O 1,4

%A _Gary W. Adamson_, May 03 2009