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Triangle read by rows: the matrix product A158821 * A051731.
1

%I #13 Jan 08 2015 15:21:32

%S 1,2,1,3,0,1,4,1,0,1,5,0,0,0,1,6,1,1,0,0,1,7,0,0,0,0,0,1,8,1,0,1,0,0,

%T 0,1,9,0,1,0,0,0,0,0,1,10,1,0,0,1,0,0,0,0,1,11,0,0,0,0,0,0,0,0,0,1,12,

%U 1,1,1,0,1,0,0,0,0,0,1

%N Triangle read by rows: the matrix product A158821 * A051731.

%F Triangle read by rows, A158821 * A051731, where A051731 = the inverse Mobius transform.

%F T(n,k) = A051731(n,k) if k>1.

%F T(n,1) = n.

%e First few rows of the triangle =

%e 1;

%e 2, 1;

%e 3, 0, 1;

%e 4, 1, 0, 1;

%e 5, 0, 0, 0, 1;

%e 6, 1, 1, 0, 0, 1;

%e 7, 0, 0, 0, 0, 0, 1;

%e 8, 1, 0, 1, 0, 0, 0, 1;

%e 9, 0, 1, 0, 0, 0, 0, 0, 1;

%e 10, 1, 0, 0, 1, 0, 0, 0, 0, 1;

%e 11, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1;

%e 12, 1, 1, 1, 0, 1, 0, 0, 0, 0, 0, 1;

%e 13, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1;

%e ...

%p N:= 20: # to get the first N rows

%p M1:= Matrix(N,N, shape = triangular[lower]);

%p M1[..,1] := Vector([$0..N-1]);

%p M1:= M1 + LinearAlgebra:-IdentityMatrix(N);

%p M2:= Matrix(N,N, shape=triangular[lower],(i,j) -> charfcn[0](i mod j));

%p M:= M1 . M2;

%p seq(seq(M[i,j],j=1..i),i=1..N); # _Robert Israel_, Jan 08 2015

%Y Cf. A158821, A051731, A158907 (row sums).

%K nonn,tabl

%O 1,2

%A _Gary W. Adamson_ and _Mats Granvik_, Mar 29 2009