OFFSET
0,1
LINKS
Colin Barker, Table of n, a(n) for n = 0..1000
D. W. Boyd, Pisot sequences which satisfy no linear recurrences, Acta Arith. 32 (1) (1977) 89-98
D. W. Boyd, Some integer sequences related to the Pisot sequences, Acta Arithmetica, 34 (1979), 295-305
D. W. Boyd, On linear recurrence relations satisfied by Pisot sequences, Acta Arithm. 47 (1) (1986) 13
D. W. Boyd, Pisot sequences which satisfy no linear recurrences. II, Acta Arithm. 48 (1987) 191
D. W. Boyd, Linear recurrence relations for some generalized Pisot sequences, in Advances in Number Theory (Kingston ON, 1991), pp. 333-340, Oxford Univ. Press, New York, 1993; with updates from 1996 and 1999.
D. G. Cantor, On families of Pisot E-sequences, Ann. Sci. Ecole Nat. Sup. 9 (2) (1976) 283-308
FORMULA
Conjectured g.f.: (-x^5+x^4-x^3+x^2-2*x+3)/((1-x)*(1-2*x-x^3-x^5)). - Ralf Stephan, May 12 2004
I believe that David Boyd has proved that this g.f. is correct. - N. J. A. Sloane, Aug 11 2016
MATHEMATICA
RecurrenceTable[{a[0] == 3, a[1] == 7, a[n] == Floor[a[n - 1]^2/a[n - 2]]}, a, {n, 0, 40}] (* Bruno Berselli, Feb 04 2016 *)
nxt[{a_, b_}]:={b, Floor[b^2/a]}; NestList[nxt, {3, 7}, 30][[All, 1]] (* Harvey P. Dale, Oct 11 2020 *)
PROG
(Magma) Iv:=[3, 7]; [n le 2 select Iv[n] else Floor(Self(n-1)^2/Self(n-2)): n in [1..40]]; // Bruno Berselli, Feb 04 2016
(PARI) pisotT(nmax, a1, a2) = {
a=vector(nmax); a[1]=a1; a[2]=a2;
for(n=3, nmax, a[n] = floor(a[n-1]^2/a[n-2]));
a
}
pisotT(50, 3, 7) \\ Colin Barker, Jul 29 2016
CROSSREFS
KEYWORD
nonn
AUTHOR
STATUS
approved