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

0, 1, 4, 85, 621436, 239988219843053389, 13821964488793901254190711941736196403535171578341580

Offset

0,3

Comments

The next term has 157 digits. - Harvey P. Dale, Dec 08 2019

References

Mordechai Ben-Ari, Mathematical Logic for Computer Science, Third edition, 173-203

Links

Table of n, a(n) for n=0..6.

Wikipedia, Herbrand Structure

Damiano Zanardini, Computational Logic, UPM European Master in Computational Logic (EMCL) School of Computer Science Technical University of Madrid.

Formula

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

a(2n) mod 2 = 0 ; a(2n+1) mod 2 = 1. - Altug Alkan, Oct 04 2015

Example

a(3) = 4^3 + 4^2 + 4 + 1 = 64 + 16 + 4 + 1 = 85.

Mathematica

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 *)
NestList[#^3+#^2+#+1&, 0, 7] (* Harvey P. Dale, Dec 08 2019 *)

Prog

(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
(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
(PARI) a(n) = if(n==0, 0, a(n-1)^3 + a(n-1)^2 + a(n-1) + 1);
vector(10, n, a(n-1)) \\ Altug Alkan, Oct 06 2015

Crossrefs

Cf. A002065.

Sequence in context: A189831 A223955 A116330 * A055591 A055764 A163279

Adjacent sequences: A055773 A055774 A055775 * A055777 A055778 A055779

Keyword

nonn

Author

Henry Bottomley, Jul 12 2000

Extensions

Next term is too big to include.

Status

approved