Can anyone identify these constants?

[Paul D. Hanna]

> Limit[Log[10, Hypergeometric2F1[(1/2)*(1 - n), (-(1/2))*n, 2, 4]]/n, n
-> Infinity]
> http://www.research.att.com/projects/OEIS?Anum=A114473
> 0.47712...
 
Limit[a(n)/10^n,n->Infinity] = Log[10, 3 ] 
= 0.477121254719662437295027903...
 
since the real root possessing the smallest absolute value 
of expression (1-2*x-3*x^2) (found in the g.f.) equals 1/3.
 
> Limit[Log[10, Hypergeometric2F1[-n + 1, n + 2, 2, -1]]/n, n ->
Infinity]
> Limit[Log[10, Hypergeometric2F1[-n + 1, n + 1, 1, -1]]/n, n ->
Infinity]
> http://www.research.att.com/projects/OEIS?Anum=A114470
> http://www.research.att.com/projects/OEIS?Anum=A114472
> 0.76555...
> 
 
Limit[a(n)/10^n,n->Infinity] = Log[10, 3+2*sqrt(2) ] 
= 0.765551370675726156638799048...
 
since the real root possessing the smallest absolute value 
of expression (1-6*x+x^2) (found in the g.f.) equals 1/(3+2*sqrt(2)).
 
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