A232806 - OEIS

%I #28 Oct 31 2025 11:55:22

%S 1,3,7,27,367,67347,2267809207,2571479299676984427,

%T 3306252894333617140505030630200259167,

%U 5465654100644710254338412340877627345031115357273557843293337076983766947

%N a(n) = a(n-1)^2/2 + 5/2,  a(0) = 1.

%C First differences are 2*A063573.

%H Andrew Howroyd, <a href="/A232806/b232806.txt">Table of n, a(n) for n = 0..12</a>

%F a(n) = 2*A002065(n) + 1.

%F a(n) = 2*A166105(n) - 1. - _Robert FERREOL_, May 31 2020

%F a(n) = A002065(n) + A166105(n). - _Alois P. Heinz_, Jun 07 2020

%t NestList[(5 + #^2)/2 &, 1, 10] (* _Paolo Xausa_, Oct 31 2025 *)

%o (PARI) a(n) = my(x=1); for(n=1, n, x = (x^2 + 5)/2); x \\ _Andrew Howroyd_, Oct 30 2025

%Y Cf. A063573, A002065, A166105.

%K nonn

%O 0,2

%A _Richard R. Forberg_, Nov 30 2013

%E a(9) added by _Andrew Howroyd_, Oct 30 2025