A276693 a(n) = a(n-2)*a(n-3) - a(n-1); a(0) = 3, a(1) = 5, a(2) = 7.

3, 5, 7, 8, 27, 29, 187, 596, 4827, 106625, 2770267, 511908608, 294867810267, 1417828655948069, 150943952469132130267, 418071880169258361764894156, 214012660834726939177944668730210267, 63105422008735225121538219609433904551328809385

Offset: 0

Author

Christopher C. Capobianco, Sep 13 2016

Keywords

• nonn

Links

• Harvey P. Dale, Table of n, a(n) for n = 0..27

Programs

C

int seq(int n) {int v = 3; if(n <= 2) {v = 3+2*n;} else {v = seq(n-2)*seq(n-3) - seq(n-1);} return v;}

Mathematica

RecurrenceTable[{a[n] ==  a[n-2]*a[n-3]-a[n-1], a[0] == 3,a[1]==5,a[2]==7}, a, {n,0, 17}]
nxt[{a_,b_,c_}]:={b,c,a*b-c}; NestList[nxt,{3,5,7},20][[All,1]] (* Harvey P. Dale, May 27 2020 *)

Formula

a(n) ~ c^(d^n), where c = 2.46982021132238000769..., d = A060006 = (1/2+sqrt(23/108))^(1/3) + (1/2-sqrt(23/108))^(1/3) = 1.32471795724474602596..., real root of the equation d*(d^2-1) = 1. - Vaclav Kotesovec, Oct 04 2016