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A195503 Numerators b(n) of Pythagorean approximations b(n)/a(n) to sqrt(3). 5

%I #34 Jun 30 2023 18:49:33

%S 4,15,56,209,780,2911,10864,40545,151316,564719,2107560,7865521,

%T 29354524,109552575,408855776,1525870529,5694626340,21252634831,

%U 79315912984,296011017105,1104728155436,4122901604639,15386878263120,57424611447841

%N Numerators b(n) of Pythagorean approximations b(n)/a(n) to sqrt(3).

%C See A195500 for discussion and list of related sequences; see A195499 for Mathematica program.

%C Essentially the same as A001353, A106707, A125905 and likely also A010905. - R. J. Mathar, Sep 21 2011

%C If started 1, 4, 15, 56, ...., denominators a(n) of Pythagorean approximations b(n)/a(n) to sqrt(1/3). - Clark Kimberling, Sep 22 2011

%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (4, -1).

%F a(n) = A001353(n+1). - R. J. Mathar, Sep 21 2011

%F Empirical G.f.: x*(4-x)/(1-4*x+x^2). - Colin Barker, Jan 04 2012

%Y Cf. A195500, A195499, A195531.

%K nonn,easy

%O 1,1

%A _Clark Kimberling_, Sep 20 2011

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