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A153462
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Triangle read by rows, = A000931(n-k+3) * (A000073 * 0^(n-k))
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2
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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
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 3,10
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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.
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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.
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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).
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CROSSREFS
| Cf. A000931, A000073
Sequence in context: A127284 A120691 A111941 * A126310 A109086 A105794
Adjacent sequences: A153459 A153460 A153461 * A153463 A153464 A153465
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KEYWORD
| nonn,tabl
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AUTHOR
| Gary W. Adamson (qntmpkt(AT)yahoo.com), Dec 27 2008
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