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Search: id:A117918
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| A117918 |
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Difference row triangle of the Pell sequence. |
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+0
1
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| 1, 1, 2, 2, 3, 5, 2, 4, 7, 12, 4, 6, 10, 17, 29, 4, 8, 14, 24, 41, 70, 8, 12, 20, 34, 58, 99, 169, 8, 16, 28, 48, 82, 140, 239, 408, 16, 24, 40, 68, 116, 198, 338, 577, 985, 16, 32, 56, 96, 164, 280, 478, 816, 1393, 2378, 32, 48, 80, 136, 232, 396, 676, 1154, 1970, 3363, 5741
(list; graph; listen)
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OFFSET
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1,3
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COMMENT
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Leftmost column (1, 1, 2, 2, 4, 4,...), (A016116); is the inverse binomial transform of the Pell sequence.
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REFERENCES
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Raymond Lebois, "Le theoreme de Pythagore et ses implications", p. 123, Editions PIM, (1979).
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FORMULA
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Difference rows of the Pell sequence A000129 starting (1, 2, 5, 12...) become the diagonals of the triangle A117918.
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EXAMPLE
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Right border = the Pell sequence. First difference row (1, 3, 7, 17, 41...) is the next diagonal.
First few rows of the triangle are:
1;
1, 2;
2, 3, 5;
2, 4, 7, 12;
4, 6, 10, 17, 29;
4, 8, 14, 24, 41, 70;
8, 12, 20, 34, 58, 99, 169;
...
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CROSSREFS
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Cf. A000129, A016116.
Adjacent sequences: A117915 A117916 A117917 this_sequence A117919 A117920 A117921
Sequence in context: A058256 A130725 A138117 this_sequence A039638 A090926 A023503
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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), Apr 02 2006
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