login
Denominators of the first differences of 1/(n^2 + 1).
3

%I #16 Oct 15 2024 15:43:02

%S 2,10,10,170,442,962,1850,650,5330,8282,12322,17690,986,33490,44522,

%T 58082,74530,18850,117650,145162,177242,214370,51410,305810,361202,

%U 423802,494210,114610,660970,758642

%N Denominators of the first differences of 1/(n^2 + 1).

%H G. C. Greubel, <a href="/A033466/b033466.txt">Table of n, a(n) for n = 0..2000</a>

%F For all n not in A016873, a(n) = n^4 + 2n^3 + 3n^2 + 2n + 2, else A099024((n-2)/5). - _Ralf Stephan_, Sep 25 2004

%F a(n) = denominator of (2*n+1)/((n^2+1)*((n+1)^2+1)). - _G. C. Greubel_, Oct 14 2024

%t Table[Denominator[(1+2*n)/((1+n^2)*(1+(n+1)^2))], {n,0,40}] (* _G. C. Greubel_, Oct 14 2024 *)

%o (Magma)

%o A033466:= func< n | Denominator((2*n+1)/((n^2+1)*((n+1)^2+1))) >;

%o [A033466(n): n in [0..40]]; // _G. C. Greubel_, Oct 14 2024

%o (SageMath)

%o def A033466(n): return denominator((2*n+1)/((n^2+1)*((n+1)^2+1)))

%o [A033466(n) for n in range(41)] # _G. C. Greubel_, Oct 14 2024

%Y Cf. A033465 (numerators).

%K nonn,frac

%O 0,1

%A _N. J. A. Sloane_