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Search: id:A117584
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| A117584 |
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Generalized Pellian triangle. |
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+0
3
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| 1, 1, 2, 1, 3, 5, 1, 4, 7, 12, 1, 5, 9, 17, 29, 1, 6, 11, 22, 41, 70, 1, 7, 13, 27, 53, 99, 169, 1, 8, 15, 32, 65, 128, 239, 408, 1, 9, 17, 37, 77, 157, 309, 577, 985, 1, 10, 19, 42, 89, 186, 379, 746, 1393, 2378
(list; graph; listen)
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OFFSET
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1,3
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COMMENT
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Diagonals of the triangle are composed of the infinite set of Pellian sequences. Right border = A000129. Next diagonal going to the left = A001333 starting (1, 3, 7, 17...). A048654 = (1, 4, 9,...). A048655 = (1, 5, 11,...). A048693 = (1, 6, 13...); and so on.
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FORMULA
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Antidiagonals of the generalized Pellian array. First row of the array = A000129: (1, 2, 5, 12...). n-th row of the array starts (1, n+1,...); as a Pellian sequence.
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EXAMPLE
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First few rows of the triangle are:
1;
1, 2;
1, 3, 5;
1, 4, 7, 12;
1, 5, 9, 17, 29;
1, 6, 11, 22, 41, 70;
1, 7, 13, 27, 53, 99, 169;
...
The triangle rows are antidiagonals of the generalized Pellian array:
1, 2, 5, 12, 29,...
1, 3, 7, 17, 41,...
1, 4, 9, 22, 53,...
1, 5, 11, 27, 65,...
...
For example, in the row (1, 5, 11, 27, 65...), 65 = 2*27 + 11.
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CROSSREFS
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Cf. A000129, A001333, A048654, A048655, A048693.
Adjacent sequences: A117581 A117582 A117583 this_sequence A117585 A117586 A117587
Sequence in context: A093412 A119355 A076110 this_sequence A047997 A049069 A030237
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KEYWORD
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nonn
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AUTHOR
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Gary W. Adamson (qntmpkt(AT)yahoo.com), Mar 29 2006
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