3,10

An eigentriangle by rows, the Padovan sequence convolved with the Tribonacci numbers.

Sum of n-th row terms = rightmost term of next row. Row sums = the Tribonacci numbers, A000073.

Triangle read by rows, = A000931(n-k+3) * (A000073* 0^(n-k)).

Equals infinite lower triangular matrices P*M; where P = a matrix with the Padovan sequence in every column starting with offset 3: (1, 0, 1, 1, 1, 2, 2, 3, 4, 5,...).

M = an infinite lower triangular matrix with the Tribonacci sequence prefaced

with a 1 as the main diagonal: (1, 1, 1, 2, 4, 7, 13,...) and the rest zeros.

First few rows of the triangle =

1;

0, 1;

1, 0, 1;

1, 1, 0, 2;

1, 1, 1, 0, 4;

2, 1, 1, 2, 0, 7;

2, 2, 1, 2, 4, 0, 13;

3, 2, 2, 2, 4, 7, 0, 24;

4, 3, 2, 4, 4, 7, 13, 0, 44;

5, 4, 3, 4, 8, 7, 13, 24, 0, 81;

7, 5, 4, 6, 8, 14, 13, 24, 44, 0, 149;

9, 7, 5, 8, 12, 14, 26, 24, 44, 81, 0, 274;

12, 9, 7, 10, 16, 21, 26, 48, 44, 81, 149, 0, 504;

...

Row 9 = (2, 2, 1, 2, 4, 0, 13) = termwise products of (1, 1, 1, 2, 4, 7, 13) and (2, 2, 1, 1, 1, 0, 1). Dot product = 24 = A000073(8).

Cf. A000931, A000073

Sequence in context: A127284 A120691 A111941 this_sequence A126310 A109086 A105794

Adjacent sequences: A153459 A153460 A153461 this_sequence A153463 A153464 A153465

nonn,tabl

Gary W. Adamson (qntmpkt(AT)yahoo.com), Dec 27 2008