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A117473 The values of 'a' in a^2 + b^2 = c^2, where b - a = 17 and gcd(a, b, c) = 1. 1

%I

%S 7,28,88,207,555,1248,3276,7315,19135,42676,111568,248775,650307,

%T 1450008,3790308,8451307,22091575,49257868,128759176,287095935,

%U 750463515,1673317776,4374021948,9752810755,25493668207

%N The values of 'a' in a^2 + b^2 = c^2, where b - a = 17 and gcd(a, b, c) = 1.

%C b - a = 17 is the third term in A058529.

%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (1,6,-6,-1,1).

%F a(1) = 7, a(2) = 28, a(3) = 207, a(4) = 555, a(n) = 6*a(n-2) - a(n-4) + 34.

%F G.f.: x*(5*x^4 + 7*x^3 - 18*x^2 - 21*x - 7) / ((x-1)*(x^2 - 2*x - 1)*(x^2 + 2*x - 1)). - _Colin Barker_, Dec 17 2012

%e a(5) = 6*88 - 7 + 34 = 555 and 555^2 + 572^2 = 797^2 and 572 - 555 = 17 and gcd(555, 572, 797) = 1.

%t CoefficientList[Series[(5x^4 + 7x^3 - 18x^2 - 21x - 7)/((x - 1)(x^2 - 2x - 1)(x^2 + 2x - 1)), {x, 0, 30}], x] (* _Wesley Ivan Hurt_, Apr 14 2017 *)

%t LinearRecurrence[{1,6,-6,-1,1},{7,28,88,207,555},30] (* _Harvey P. Dale_, Jul 31 2017 *)

%Y Cf. A058529, A117472.

%K nonn,easy

%O 1,1

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

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Last modified June 15 04:47 EDT 2021. Contains 345043 sequences. (Running on oeis4.)