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%I #20 Feb 26 2024 01:54:41
%S 1,25,1201,58825,2882401,141237625,6920643601,339111536425,
%T 16616465284801,814206798955225,39896133148806001,1954910524291494025,
%U 95790615690283207201,4693740168823877152825,229993268272369980488401,11269670145346129043931625
%N Sequence demonstrating the Pythagorean theorem.
%H G. C. Greubel, <a href="/A120694/b120694.txt">Table of n, a(n) for n = 0..500</a>
%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (50,-49).
%F sqrt((a(n)^2 - (a(n)-1)^2)) = 7^n.
%F a(n) = 50*a(n-1) - 49*a(n-2).
%F a(n) = (1/2)*(1 + 49^n).
%F G.f.: (1-25*x)/(1-10*x+49*x^2). - _Harvey P. Dale_, Dec 31 2011
%F E.g.f.: (1/2)*(exp(x) + exp(49*x)). - _G. C. Greubel_, Dec 28 2022
%t LinearRecurrence[{50,-49},{1,25},21] (* _Harvey P. Dale_, Dec 31 2011 *)
%o (Magma) [(1+(49)^n)/2: n in [0..20]]; // _G. C. Greubel_, Dec 28 2022
%o (SageMath) [(1+(49)^n)/2 for n in range(21)] # _G. C. Greubel_, Dec 28 2022
%K nonn
%O 0,2
%A _Gary W. Adamson_, Jun 28 2006
%E More terms from _Harvey P. Dale_, Dec 31 2011
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