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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
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
KEYWORD
nice,nonn,easy
AUTHOR
Lekraj Beedassy, Apr 29 2005
STATUS
approved