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

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 =
   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).

Crossrefs

Cf. A000073, A000931.

Sequence in context: A127284 A120691 A111941 * A126310 A109086 A213620

Adjacent sequences: A153459 A153460 A153461 * A153463 A153464 A153465

Keyword

nonn,tabl

Author

Gary W. Adamson, Dec 27 2008

Status

approved