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A055776 a(n) = a(n-1)^3 + a(n-1)^2 + a(n-1) + 1.

%I A055776 #48 Sep 08 2022 08:45:01
%S A055776 0,1,4,85,621436,239988219843053389,
%T A055776 13821964488793901254190711941736196403535171578341580
%N A055776 a(n) = a(n-1)^3 + a(n-1)^2 + a(n-1) + 1.
%C A055776 The next term has 157 digits. - _Harvey P. Dale_, Dec 08 2019
%D A055776 Mordechai Ben-Ari, Mathematical Logic for Computer Science, Third edition, 173-203
%H A055776 Wikipedia, <a href="https://en.wikipedia.org/wiki/Herbrand_structure">Herbrand Structure</a>
%H A055776 Damiano Zanardini, <a href="http://costa.fdi.ucm.es/~damiano/teaching/emcl/cl_08_09/slides/12lprog.pdf">Computational Logic</a>, UPM European Master in Computational Logic (EMCL) School of Computer Science Technical University of Madrid.
%F A055776 a(n) is asymptotic to c^(3^(n+1)) where c=1.056431004248312118265251254776175173104598976924006344252579493163876246969557582... - _Gerald McGarvey_, Dec 08 2007, corrected by _Vaclav Kotesovec_, Apr 03 2016
%F A055776 a(2n) mod 2 = 0 ; a(2n+1) mod 2 = 1. - _Altug Alkan_, Oct 04 2015
%e A055776 a(3) = 4^3 + 4^2 + 4 + 1 = 64 + 16 + 4 + 1 = 85.
%t A055776 RecurrenceTable[{a[n] == a[n - 1]^3 + a[n - 1]^2 + a[n - 1] + 1, a[0] == 0}, a, {n, 0, 6}] (* _Michael De Vlieger_, Oct 05 2015 *)
%t A055776 NestList[#^3+#^2+#+1&,0,7] (* _Harvey P. Dale_, Dec 08 2019 *)
%o A055776 (PARI) a=vector(6);a[1]=1;print1("0, 1, ");for(n=2,6,a[n]=a[n-1]^3+a[n-1]^2+a[n-1]+1;print1(a[n],", ")) \\ _Gerald McGarvey_, Dec 08 2007
%o A055776 (Magma) [n le 1 select 0 else Self(n-1)^3 + Self(n-1)^2 + Self(n-1) + 1: n in [1..15]]; // _Vincenzo Librandi_, Oct 05 2015
%o A055776 (PARI) a(n) = if(n==0, 0, a(n-1)^3 + a(n-1)^2 + a(n-1) + 1);
%o A055776 vector(10, n, a(n-1)) \\ _Altug Alkan_, Oct 06 2015
%Y A055776 Cf. A002065.
%K A055776 nonn
%O A055776 0,3
%A A055776 _Henry Bottomley_, Jul 12 2000
%E A055776 Next term is too big to include.