|
|
A020746
|
|
Pisot sequence T(3,7), a(n) = floor(a(n-1)^2/a(n-2)).
|
|
3
|
|
|
3, 7, 16, 36, 81, 182, 408, 914, 2047, 4584, 10265, 22986, 51471, 115255, 258081, 577899, 1294040, 2897633, 6488421, 14528964, 32533461, 72849384, 163125366, 365272615, 817923579, 1831505986, 4101133972, 9183316890, 20563412382, 46045882316, 103106587509
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,1
|
|
LINKS
|
|
|
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
}
|
|
CROSSREFS
|
See A008776 for definitions of Pisot sequences.
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|