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A077020 a(n) is the unique odd positive solution x of 2^n = 7x^2+y^2. 11

%I

%S 1,1,1,3,1,5,7,3,17,11,23,45,1,91,89,93,271,85,457,627,287,1541,967,

%T 2115,4049,181,8279,7917,8641,24475,7193,41757,56143,27371,139657,

%U 84915,194399,364229,24569,753027,703889,802165,2209943,605613

%N a(n) is the unique odd positive solution x of 2^n = 7x^2+y^2.

%C The sequences A001607, A077020, A107920, A167433, A169998 are all essentially the same except for signs.

%D A. Engel, Problem-Solving Strategies. p. 126.

%H T. D. Noe, <a href="/A077020/b077020.txt">Table of n, a(n) for n=3..500</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/DiophantineEquation2ndPowers.html">Diophantine Equations 2nd Powers</a>

%F a(n) = 2^(n-2) * a(4-n) for all n in Z. - _Michael Somos_, Jan 05 2017

%F 0 = 8*a(n)^2 + 2*a(n+1)^2 - a(n+2)^2 - a(n+3)^2 for all n in Z. - _Michael Somos_, Jan 05 2017

%F 2*a(n) + a(n+1) = a(n+2) or a(n+3). - _Michael Somos_, Jan 05 2017

%e G.f. = x^3 + x^4 + x^5 + 3*x^6 + x^7 + 5*x^8 + 7*x^9 + 3*x^10 + 17*x^11 + ...

%e a(3)=1 since 2^3=8=7*1^2+1^2, a(6)=3 since 2^6=64=7*3^2+1^2.

%Y a(n)=abs(A001607(n-2)).

%Y Cf. A077021.

%K nonn

%O 3,4

%A _Ed Pegg Jr_, Oct 17 2002

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Last modified October 1 08:39 EDT 2020. Contains 337442 sequences. (Running on oeis4.)