1,5

First row of the array = the Fredholm-Rueppel sequence (A036987); which becomes the right border of the triangle. Second row of the array (1, 2, 0, 3, 0, 0, 0, 4,...) = A104117. Third row of the array (1, 3, 0, 6, 0, 0, 0, 10,...) = A129502. Row sums of triangle A129503 = A129504: (1, 2, 3, 5, 8, 12, 17, 24, 34,...).

Antidiagonals of an array in which n-th row (n=0,1,2,...) = M^n * V, where M = A115361 as an infinite lower triangular matrix and V = the Fredholm-Rueppel sequence A036987 as a vector: [1, 1, 0, 1, 0, 0, 0, 1,...]. The array = 1, 1, 0, 1, 0, 0, 0, 1, 0,... 1, 2, 0, 3, 0, 0, 0, 4, 0,... 1, 3, 0, 6, 0, 0, 0, 10, 0,... 1, 4, 0, 10, 0, 0, 0, 20, 0,... .. (n+1)-th row can be generated from A115361 * n-th row.

First few rows of the triangle are:

1;

1, 1;

1, 2, 0;

1, 3, 0, 1;

1, 4, 0, 3, 0;

1, 5, 0, 6, 0, 0;

1, 6, 0, 10, 0, 0, 0;

1, 7, 0, 15, 0, 0, 0, 1;

1, 8, 0, 21, 0, 0, 0, 4, 0;

1, 9, 0, 28, 0, 0, 0, 1, 0, 0, 0;

1, 10, 0, 36, 0, 0, 0, 20, 0, 0, 0;

...

Cf. A036987, A115361, A104117, A129502, A129504.

Sequence in context: A119900 A141097 A096335 this_sequence A144185 A143987 A112760

Adjacent sequences: A129500 A129501 A129502 this_sequence A129504 A129505 A129506

nonn,tabl

Gary W. Adamson (qntmpkt(AT)yahoo.com), Apr 18 2007