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 A120694 Sequence demonstrating the Pythagorean theorem. 1

%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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Last modified August 6 03:16 EDT 2024. Contains 374957 sequences. (Running on oeis4.)