A106318 Bhaskara twins: n such that 2*n^2 = X^3 and 2*n^3 = Y^2.
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
References
- S. S. Gupta, 'Bhaskara Pairs' in 'Science Today' (subsequently renamed '2001'), January 1988, pp. 68, Times of India, Mumbai.
Links
- Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
- Richard J. Mathar, Construction of Bhaskara Pairs, arXiv:1703.01677 [math.NT], 2017.
- Index entries for linear recurrences with constant coefficients, signature (7,-21,35,-35,21,-7,1).
Programs
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Haskell
a106318 = (* 2) . (^ 6) -- Reinhard Zumkeller, May 27 2015
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Mathematica
LinearRecurrence[{7,-21,35,-35,21,-7,1},{2,128,1458,8192,31250,93312,235298},30] (* Harvey P. Dale, May 11 2017 *) -
PARI
a(n)=2*n^6 \\ Charles R Greathouse IV, Feb 09 2012
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