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 A160756 Triangle read by rows, infinite lower triangular Toeplitz matrix with A078008 in every column convolved with A001333. 1

%I

%S 1,0,1,2,0,1,2,2,0,3,6,2,2,0,7,10,6,2,6,0,17,22,10,6,6,14,0,41,42,22,

%T 10,18,14,34,0,99,86,42,22,30,42,34,82,0,239,170,86,42,66,70,102,82,

%U 198,0,577

%N Triangle read by rows, infinite lower triangular Toeplitz matrix with A078008 in every column convolved with A001333.

%C Row sums = A001333: (1, 1, 3, 7, 17, 41,...). Sum of n-th row terms = rightmost term of next row.

%F Let M = an infinite lower triangular Toeplitz matrix with A078008 (1, 0, 2, 2, 6, 10, 22, 42, 86, 170,...). Let Q = the eigensequence of that triangle prefaced with a 1: (1, 1, 1, 3, 7, 17,...) where A001333 = (1, 1, 3, 7, 17,...). The triangle = M * Q.

%e First few rows of the triangle =

%e 1;

%e 0, 1;

%e 2, 0, 1;

%e 2, 2, 0, 3;

%e 6, 2, 2, 0, 7;

%e 10, 6, 2, 6, 0, 17;

%e 22, 10, 6, 6, 14, 0, 41;

%e 42, 22, 10, 18, 14, 34, 0, 99;

%e 86, 42, 22, 30, 42, 34, 82, 0, 239;

%e 170, 86, 42, 66, 70, 102, 82, 198, 0, 577;

%e ...

%e Example: row 4 = (6, 2, 2, 0, 7) = (6, 2, 2, 0, 1) * (1, 1, 1, 3, 7).

%Y Cf. A078008, A001333

%K nonn,tabl

%O 0,4

%A _Gary W. Adamson_, May 25 2009

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