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1, 0, 2, 1, 0, 3, 0, 4, 0, 4, 1, 0, 10, 0, 5, 0, 6, 0, 20, 0, 6, 1, 0, 21, 0, 35, 0, 7, 0, 8, 0, 56, 0, 56, 0, 8, 1, 0, 36, 0, 126, 0, 84, 0, 9
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 1,3
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COMMENTS
| Row sums = (1, 2, 4, 8,...). A131047 * (1,2,3,...) = A087447 starting (1, 4, 10, 24, 56,...). A generalized set of analogous triangles: ((1/(Q+1)) * (P^Q - 1/P), Q an integer, generates triangles with row sums = powers of (Q+1). Cf. A131048, A131049, A131050, A131051 for triangles having Q = 2,3,4 and 5, respectively.
A007318, Pascal's triangle, = this triangle + A119467, since one triangle = the zeros or masks of the other. - Gary W. Adamson (qntmpkt(AT)yahoo.com), Jun 12 2007
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FORMULA
| Let A007318 (Pascal's triangle) = P, then A131047 = (1/2) * (P - 1/P); deleting the right border of zeros.
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EXAMPLE
| First few rows of the triangle are:
1;
0, 2;
1, 0, 3;
0, 4, 0, 4;
1, 0, 10, 0, 5;
0, 6, 0, 20, 0, 6;
1, 0, 21, 0, 35, 0, 7;
...
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CROSSREFS
| Cf. A131048, A131049, A131050, A131051.
Cf. A119467.
Sequence in context: A123973 A098493 A058560 * A143714 A004172 A082754
Adjacent sequences: A131044 A131045 A131046 * A131048 A131049 A131050
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KEYWORD
| nonn,tabl
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AUTHOR
| Gary W. Adamson (qntmpkt(AT)yahoo.com), Jun 12 2007
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