A033466 Denominators of the first differences of 1/(n^2 + 1).

2, 10, 10, 170, 442, 962, 1850, 650, 5330, 8282, 12322, 17690, 986, 33490, 44522, 58082, 74530, 18850, 117650, 145162, 177242, 214370, 51410, 305810, 361202, 423802, 494210, 114610, 660970, 758642

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• frac

Links

• G. C. Greubel, Table of n, a(n) for n = 0..2000

Crossrefs

Cf. A033465 (numerators).

Programs

Magma

A033466:= func< n | Denominator((2*n+1)/((n^2+1)*((n+1)^2+1))) >;
[A033466(n): n in [0..40]]; // G. C. Greubel, Oct 14 2024

Mathematica

Table[Denominator[(1+2*n)/((1+n^2)*(1+(n+1)^2))], {n,0,40}] (* G. C. Greubel, Oct 14 2024 *)

SageMath

def A033466(n): return denominator((2*n+1)/((n^2+1)*((n+1)^2+1)))
[A033466(n) for n in range(41)] # G. C. Greubel, Oct 14 2024

Formula

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

a(n) = denominator of (2*n+1)/((n^2+1)*((n+1)^2+1)). - G. C. Greubel, Oct 14 2024