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A028945
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A006720(n)^2 (squared terms of Somos-4 sequence).
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3
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1, 1, 1, 1, 4, 9, 49, 529, 3481, 98596, 2337841, 67387681, 6941055969, 384768368209, 61935294530404, 16063784753682169, 2846153597907293521, 2237394491744632911601, 1262082793174195430038441, 1063198259901027900600665796
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,5
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COMMENTS
| If first two 1's are omitted, denominator of x coordinate of 2n*P where P is generator for rational points on curve y^2+y = x^3-x.
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REFERENCES
| B. Mazur, Arithmetic on curves, Bull. Amer Math. Soc. 14 (1986), 207-259; see p 225.
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FORMULA
| P=(0, 0), 2P=(1, 0), if kP=(a, b) then (k+1)P=(a'=(b^2-a^3)/a^2, b'=1-b*a'/a).
a(n) = (- 4 a(n - 6) a(n - 1) + 29 a(n - 5) a(n - 2) + 116 a(n - 4) a(n - 3))/a(n-7). - R. W. Gosper, May 14 2009
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CROSSREFS
| Cf. A006720, A028935.
Sequence in context: A030088 A081069 A053967 * A082875 A086541 A053965
Adjacent sequences: A028942 A028943 A028944 * A028946 A028947 A028948
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KEYWORD
| nonn,frac
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
| Edited by N. J. A. Sloane (njas(AT)research.att.com), May 14 2009
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