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The values of a in a^2 + b^2 = c^2 where b - a = 23 and gcd(a,b,c)=1.
1

%I #8 Jun 13 2015 00:52:05

%S 12,33,133,252,832,1525,4905,8944,28644,52185,167005,304212,973432,

%T 1773133,5673633,10334632,33068412,60234705,192736885,351073644,

%U 1123352944,2046207205,6547380825,11926169632,38160932052,69510810633

%N The values of a in a^2 + b^2 = c^2 where b - a = 23 and gcd(a,b,c)=1.

%C Values of c are in A117475

%H <a href="/index/Rec">Index entries for linear recurrences with constant coefficients</a>, signature (1,6,-6,-1,1).

%F a(1)=12, a(2)=33, a(3)=133, a(4)=252, a(n) = 6*a(n-2) - a(n-4) + 46.

%F G.f.: x*(8*x^4+7*x^3-28*x^2-21*x-12) / ((x-1)*(x^2-2*x-1)*(x^2+2*x-1)). [_Colin Barker_, Dec 17 2012]

%e a(5) = 6*133 - 12 + 46 = 832 and 832^2 + 855^2 = 1193^2 and 855-832=23 and gcd(832,855,1193)=1

%Y Cf. A117475.

%K nonn,easy

%O 1,1

%A Andras Erszegi (erszegi.andras(AT)chello.hu), Mar 19 2006