A153462 - OEIS

A153462

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

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

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OFFSET

3,10

COMMENTS

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.

LINKS

Table of n, a(n) for n=3..80.

FORMULA

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.

EXAMPLE

First few rows of the triangle =

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;