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Triangle read by rows, = A000931(n-k+3) * (A000073 * 0^(n-k))
2

%I #17 Jul 21 2021 22:49:05

%S 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,

%T 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,

%U 44,0,149,9,7,5,8,12,14,26,24,44,81,0,274

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

%C An eigentriangle by rows, the Padovan sequence convolved with the tribonacci numbers.

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

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

%F 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, ...).

%F 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.

%e First few rows of the triangle =

%e 1;

%e 0, 1;

%e 1, 0, 1;

%e 1, 1, 0, 2;

%e 1, 1, 1, 0, 4;

%e 2, 1, 1, 2, 0, 7;

%e 2, 2, 1, 2, 4, 0, 13;

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

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

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

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

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

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

%e ...

%e 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).

%Y Cf. A000073, A000931.

%K nonn,tabl

%O 3,10

%A _Gary W. Adamson_, Dec 27 2008