3,4

Row sums and right border = the Padovan sequence, A000931 starting with offset

3: (1, 1, 0, 1, 1, 1, 2, 2, 3,...).

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

Triangle read by rows, T * Q, where T = an infinite lower triangular matrix with (1, -1, 2, -2, 3, -3,...) in every column and Q = an infinite lower triangular

matrix with the Padovan sequence, A000931 as the main diagonal starting with

offset 3: (1, 1, 0, 1, 1, 1, 2, 2, 3,...). The rest of triangle Q = all zeros.

Triangle A146973 = T * Q.

First few rows of the triangle =

1;

-1, 1;

2, -1, 0;

-2, 2, 0, 1;

3, -2, 0, -1, 1;

-3, 3, 0, 2, -1, 1;

4, -3, 0, -2, 2, -1, 2;

-4, 4, 0, 3, -2, 2, -2, 2;

5, -4, 0, -3, 3, -2, 4, -2, 3;

-5, 5, 0, 4, -3, 3, -4, 4, -3, 4;

6, -5, 0, -4, 4, -3, 6, -4, 6, -4, 5;

-6, 6, 0, 5, -4, 4, -6, 6, -6, 8, -5, 7;

7, -6, 0, -5, 5, -4, 8, -6, 9, -8, 10, -7, 9

-7, 7, 0, 6, -5, 5, -8, 8, -9, 12, -10, 14, -9, 12;

...

Row 6 = (-2, 2, 0, 1) = termwise products of (-2, 2, 0, 1) and (1, 1, 0, 1).

A000931

Sequence in context: A003985 A157237 A065676 this_sequence A003263 A157242 A135211

Adjacent sequences: A146970 A146971 A146972 this_sequence A146974 A146975 A146976

eigen,tabl,sign

Gary W. Adamson (qntmpkt(AT)yahoo.com), Nov 03 2008