login
A022027
Define the sequence T(a(0),a(1)) by a(n+2) is the greatest integer such that a(n+2)/a(n+1) < a(n+1)/a(n) for n >= 0. This is T(2,16).
2
2, 16, 127, 1008, 8000, 63492, 503904, 3999232, 31739888, 251903488, 1999230976, 15866888256, 125927492096, 999423012864, 7931916549888, 62951622430720, 499615287394304, 3965194632954880, 31469750573916160, 249759543441752064, 1982215569002196992, 15731845549721911296
OFFSET
0,1
COMMENTS
Not to be confused with the Pisot T(2,16) sequence, which is A013730. - R. J. Mathar, Feb 13 2016
FORMULA
Conjectures: a(n) = 8*a(n-1)-4*a(n-3). G.f.: -(x^2-2) / (4*x^3-8*x+1). - Colin Barker, Sep 18 2015
a(n+1) = ceiling(a(n)^2/a(n-1))-1 for n>0. - M. F. Hasler, Feb 11 2016
MATHEMATICA
RecurrenceTable[{a[1] == 2, a[2] == 16, a[n] == Ceiling[a[n-1]^2 / a[n-2] - 1]}, a, {n, 30}] (* Vincenzo Librandi, Feb 12 2016 *)
PROG
(PARI) a=[2, 16]; for(n=2, 1000, a=concat(a, ceil(a[n]^2/a[n-1])-1)); A022027(n)=a[n+1] \\ M. F. Hasler, Feb 11 2016
(Magma) I:=[2, 16]; [n le 2 select I[n] else Ceiling(Self(n-1)^2/Self(n-2))-1: n in [1..30]]; // Vincenzo Librandi, Feb 12 2016
CROSSREFS
KEYWORD
nonn
AUTHOR
EXTENSIONS
Double-checked (original definition agrees with g.f. / recurrence for n=0..1000), extended and edited by M. F. Hasler, Feb 11 2016
STATUS
approved