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A106318 Bhaskara twins: n such that 2*n^2 = X^3 and 2*n^3 = Y^2. 7
2, 128, 1458, 8192, 31250, 93312, 235298, 524288, 1062882, 2000000, 3543122, 5971968, 9653618, 15059072, 22781250, 33554432, 48275138, 68024448, 94091762, 128000000, 171532242, 226759808, 296071778, 382205952, 488281250, 617831552 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
REFERENCES
S. S. Gupta, 'Bhaskara Pairs' in 'Science Today' (subsequently renamed '2001'), January 1988, pp. 68, Times of India, Mumbai.
LINKS
Richard J. Mathar, Construction of Bhaskara Pairs, arXiv:1703.01677 [math.NT], 2017.
FORMULA
a(n) = 2*n^6 = 2*A001014(n).
G.f.: 2*(1+x)*(1+56*x+246*x^2+56*x^3+x^4)/(1-x)^7. - Colin Barker, Apr 18 2012
a(n) = 7*a(n-1)-21*a(n-2)+35*a(n-3)-35*a(n-4)+21*a(n-5)-7*a(n-6)+a(n-7). - Wesley Ivan Hurt, Apr 23 2021
MATHEMATICA
LinearRecurrence[{7, -21, 35, -35, 21, -7, 1}, {2, 128, 1458, 8192, 31250, 93312, 235298}, 30] (* Harvey P. Dale, May 11 2017 *)
PROG
(PARI) a(n)=2*n^6 \\ Charles R Greathouse IV, Feb 09 2012
(Haskell)
a106318 = (* 2) . (^ 6) -- Reinhard Zumkeller, May 27 2015
CROSSREFS
Cf. A001014.
Sequence in context: A338932 A226403 A106320 * A202748 A322308 A277757
KEYWORD
nice,nonn,easy
AUTHOR
Lekraj Beedassy, Apr 29 2005
STATUS
approved

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Last modified March 28 16:12 EDT 2024. Contains 371254 sequences. (Running on oeis4.)