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

1,1

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).

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. A106319, A106320, A106321, A106322.

Cf. A001014.

Sequence in context: A338932 A226403 A106320 * A202748 A322308 A277757

Adjacent sequences: A106315 A106316 A106317 * A106319 A106320 A106321

Keyword

nice,nonn,easy

Author

Lekraj Beedassy, Apr 29 2005

Status

approved