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A104586
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Pentagonal wave sequence triangle.
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2
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1, 7, 2, 12, 5, 1, 26, 15, 7, 2, 35, 22, 12, 5, 1, 57, 40, 26, 15, 7, 2, 70, 51, 35, 22, 12, 5, 1, 100, 77, 57, 40, 26, 15, 7, 2
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| Row sums = A086500: 1, 9, 18, 50, 75, 147, 196...
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FORMULA
| Odd columns are terms of A104584, pentagonal wave sequence of the first kind, (starting with 1): 1, 7, 12, 26, 35, 57, 70... Even columns are terms of A104585, pentagonal wave sequence of the second kind (starting with 2): 2, 5, 15, 22, 40, 51... Odd rows are pentagonal numbers (A000326) starting with "1" at the right. Even rows are second pentagonal numbers (A005449) starting with 2 at the right. The triangle is extracted from a matrix product A * B, A = [1; 1, 2; 1, 2, 1; 1, 2, 1, 2;...], B = [1; 3, 1; 5, 3, 1; 7, 5, 3, 1;...] (both infinite lower triangular matrices, with the rest zeros).
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EXAMPLE
| The first few rows are:
1;
7, 2;
12, 5, 1;
26, 15, 7, 2;
35, 22, 12, 5, 1;
57, 40, 26, 15, 7, 2;
70, 51, 35, 22, 12, 5, 1;
...
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CROSSREFS
| Cf. A086500, A104584, A104585, A000326, A005449, A049452, A033570, A049453, A033568.
Sequence in context: A147677 A090243 A145338 * A040048 A070429 A050092
Adjacent sequences: A104583 A104584 A104585 * A104587 A104588 A104589
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KEYWORD
| nonn,tabl
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AUTHOR
| Gary W. Adamson (qntmpkt(AT)yahoo.com), Mar 17 2005
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