%I #21 Sep 08 2022 08:45:31
%S 1,1,1,2,3,7,43,904,272105,10577265561,2601826668310218121,
%T 7488387181338771882437732599874506,
%U 206081999881071045385328009597554265108557649484947339933019787
%N a(0)=a(1)=a(2) = 1, thereafter a(n) = a(n-1)*a(n-2)*a(n-3) + 1.
%C A tribonacci analog of A001056.
%C a(13) has 115 digits. - _R. J. Mathar_, Dec 10 2007
%H Seiichi Manyama, <a href="/A133400/b133400.txt">Table of n, a(n) for n = 0..16</a>
%F a(n) ~ c^(t^n), where c = 1.1004451797920944914628..., t = A058265 = 1.8392867552141611325518... . - _Vaclav Kotesovec_, May 05 2015
%e a(8) = a(7)*a(6)*a(5) + 1 = 904 * 43 * 7 + 1 = 272105.
%e a(9) ~ 2.60182667 * 10^18.
%e a(10) ~ 7.48838719 * 10^33.
%e a(11) ~ 2.06082 * 10^62.
%p A133400 := proc(n) local i ; if n <= 2 then 1; else 1+mul( A133400(i),i=n-3..n-1) ; fi ; end: seq(A133400(n),n=0..15) ; # _R. J. Mathar_, Dec 10 2007
%t RecurrenceTable[{a[0]==1,a[1]==1,a[2]==1, a[n] == a[n-1]*a[n-2]*a[n-3] + 1},a,{n,0,15}] (* _Vaclav Kotesovec_, May 05 2015 *)
%t nxt[{a_,b_,c_}]:={b,c,a*b*c+1}; NestList[nxt,{1,1,1},15][[All,1]] (* _Harvey P. Dale_, Mar 05 2017 *)
%o (PARI) m=15; v=concat([1,1,1], vector(m-3)); for(n=4, m, v[n]=v[n-1]*v[n-2] *v[n-3] +1 ); v \\ _G. C. Greubel_, Sep 20 2019
%o (Magma) I:=[1,1,1]; [n le 3 select I[n] else Self(n-1)*Self(n-2)* Self(n-3) + 1: n in [1..15]]; // _G. C. Greubel_, Sep 20 2019
%o (Sage)
%o def a(n):
%o if (n<3): return 1
%o else: return a(n-1)*a(n-2)*a(n-3) + 1
%o [a(n) for n in (0..15)] # _G. C. Greubel_, Sep 20 2019
%o (GAP) a:=[1,1,1];; for n in [4..15] do a[n]:=a[n-1]*a[n-2]*a[n-3]+1; od; a; # _G. C. Greubel_, Sep 20 2019
%Y Cf. A001056, A007660, A058265.
%K easy,nonn
%O 0,4
%A _Jonathan Vos Post_, Nov 24 2007, Nov 26 2007
%E More terms from _R. J. Mathar_, Dec 10 2007