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A028935 a(n) = A006720(n)^3 (cubed terms of Somos-4 sequence). 5
1, 1, 1, 1, 8, 27, 343, 12167, 205379, 30959144, 3574558889, 553185473329, 578280195945297, 238670664494938073, 487424450554237378792, 2035972062206737347698803, 4801616835579099275862827431 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,5

COMMENTS

If initial two 1's are omitted, denominator of y-coordinate of (2n+1)*P where P is the generator for rational points on the curve y^2 + y = x^3 - x.

LINKS

Seiichi Manyama, Table of n, a(n) for n = 0..88

B. Mazur, Arithmetic on curves, Bull. Amer. Math. Soc. 14 (1986), 207-259; see p. 225.

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).

EXAMPLE

5P = (1/4, -5/8).

CROSSREFS

Cf. A006720, A028934, A028943, A028945, A151502.

Sequence in context: A029792 A112993 A115694 * A030089 A007235 A029789

Adjacent sequences:  A028932 A028933 A028934 * A028936 A028937 A028938

KEYWORD

nonn

AUTHOR

N. J. A. Sloane

EXTENSIONS

Edited by N. J. A. Sloane, May 14 2009

STATUS

approved

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Last modified May 29 10:48 EDT 2017. Contains 287246 sequences.