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A250309 a(n) = a(n-1)*(1 + a(n-1)/a(n-3)), with a(0) = a(1) = a(2) = 1.

%I A250309 #24 Sep 08 2022 08:46:10
%S A250309 1,1,1,2,6,42,924,143220,488523420,258285263294520,
%T A250309 465795819523189050504840,444125576385425970712647062585372630520,
%U A250309 763680920404535561780141108036287312478667174369871222219397040
%N A250309 a(n) = a(n-1)*(1 + a(n-1)/a(n-3)), with a(0) = a(1) = a(2) = 1.
%H A250309 Seiichi Manyama, <a href="/A250309/b250309.txt">Table of n, a(n) for n = 0..17</a>
%F A250309 0 = a(n)*(a(n+2) - a(n+3)) + a(n+2)*a(n+2) for all n>=0.
%F A250309 A007660(n+1) = a(n)/a(n-1).
%F A250309 a(n) ~ b * f^(d^n), where b = 0.270887790039424376..., f = c^(2+sqrt(5)) = 1.574173161904651669837597516422779594... and d = (1+sqrt(5))/2. For the constant c = A258113 = 1.11305797590293193285359770716758491... see A007660. - _Vaclav Kotesovec_, Jan 18 2015
%t A250309 RecurrenceTable[{a[n]==a[n-1]*(1 + a[n-1]/a[n-3]), a[0]==1, a[1]==1, a[2]==1},a,{n,0,12}] (* _Vaclav Kotesovec_, Jan 18 2015 *)
%o A250309 (PARI) {a(n) = if( n<3, n>=0, a(n-1)*(1 + a(n-1)/a(n-3)))};
%o A250309 (Magma) I:=[1,1,1]; [n le 3 select I[n] else Self(n-1)*(1 + Self(n-1)/Self(n-3)): n in [1..15]]; // _G. C. Greubel_, Aug 03 2018
%Y A250309 Cf. A007660, A258113.
%K A250309 nonn
%O A250309 0,4
%A A250309 _Michael Somos_, Jan 16 2015