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Triangle read by rows, A101688 * (an infinite lower triangular matrix with A002083 as the main diagonal and the rest zeros).
1

%I #6 Jan 22 2023 08:37:08

%S 1,0,1,0,1,1,0,0,1,2,0,0,1,2,3,0,0,0,2,3,6,0,0,0,2,3,6,11,0,0,0,0,3,6,

%T 11,22,0,0,0,0,3,6,11,22,42,0,0,0,0,0,6,11,22,42,84,0,0,0,0,0,6,11,22,

%U 42,84,165,0,0,0,0,0,0,11,22,42,84,165,330

%N Triangle read by rows, A101688 * (an infinite lower triangular matrix with A002083 as the main diagonal and the rest zeros).

%C Row sums = A002083(n+1): (1, 1, 2, 3, 6, 11, 22, 42, 84, 165,...).

%C Sum of n-th row terms = rightmost term of next row.

%C Eigensequence of triangle A101688 = A002083 starting with offset 1: (1, 1, 2, 3, 6, 11, 22, 42,...).

%F Equals M * Q, where M = triangle A101688, Q = an infinite lower triangular matrix with (1, 1, 1, 2, 3, 6, 11, 22, 42,...) as the main diagonal and the rest zeros.

%e First few rows of the triangle:

%e 1;

%e 0, 1;

%e 0, 1, 1;

%e 0, 0, 1, 2;

%e 0, 0, 1, 2, 3;

%e 0, 0, 0, 2, 3, 6;

%e 0, 0, 0, 2, 3, 6, 11;

%e 0, 0, 0, 0, 3, 6, 11, 22;

%e 0, 0, 0, 0, 3, 6, 11, 22, 42;

%e 0, 0, 0, 0, 0, 6, 11, 22, 42, 84;

%e 0, 0, 0, 0, 0, 6, 11, 22, 42, 84, 165;

%e 0, 0, 0, 0, 0, 0, 11, 22, 42, 84, 165, 330;

%e 0, 0, 0, 0, 0, 0, 11, 22, 42, 84, 165, 330, 654;

%e 0, 0, 0, 0, 0, 0, .0, 22, 42, 84, 165, 330, 654, 1308;

%e 0, 0, 0, 0, 0, 0, .0, 22, 42, 84, 165, 330, 654, 1308, 2605;

%e ...

%Y Cf. A101688, A002083.

%K nonn,tabl

%O 1,10

%A _Gary W. Adamson_, Nov 15 2009