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A055776 a(n) = a(n-1)^3 + a(n-1)^2 + a(n-1) + 1. 0
0, 1, 4, 85, 621436, 239988219843053389, 13821964488793901254190711941736196403535171578341580 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

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 *)

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

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Last modified October 23 17:32 EDT 2019. Contains 328373 sequences. (Running on oeis4.)