A018917 Define the generalized Pisot 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). This is T(3,5).
3, 5, 8, 12, 17, 24, 33, 45, 61, 82, 110, 147, 196, 261, 347, 461, 612, 812, 1077, 1428, 1893, 2509, 3325, 4406, 5838, 7735, 10248, 13577, 17987, 23829, 31568, 41820, 55401, 73392, 97225, 128797, 170621, 226026, 299422, 396651, 525452, 696077, 922107
Offset: 0
Keywords
Links
- Reinhard Zumkeller, Table of n, a(n) for n = 0..1000
- D. W. Boyd, Linear recurrence relations for some generalized Pisot sequences, Advances in Number Theory ( Kingston ON, 1991) 333-340, Oxford Sci. Publ., Oxford Univ. Press, New York, 1993.
- Index entries for Pisot sequences
Programs
-
Magma
Tiv:=[3,5]; [n le 2 select Tiv[n] else Ceiling(Self(n-1)^2/Self(n-2))-1: n in [1..50]]; // Bruno Berselli, Feb 17 2016
-
Mathematica
RecurrenceTable[{a[1] == 3, a[2] == 5, a[n] == Ceiling[a[n-1]^2/a[n-2]] - 1}, a, {n, 50}] (* Bruno Berselli, Feb 17 2016 *) -
PARI
T(a0, a1, maxn) = a=vector(maxn); a[1]=a0; a[2]=a1; for(n=3, maxn, a[n]=ceil(a[n-1]^2/a[n-2])-1); a T(3, 5, 60) \\ Colin Barker, Feb 14 2016
Formula
Conjecture: a(n)=a(n-1)+a(n-2)-a(n-4). G.f.: (3+2*x-x^3)/(1-x)/(1-x^2-x^3). [Colin Barker, Feb 16 2012]
Conjecture: a(n) = a(n-1) + A000931(n+8). - Reinhard Zumkeller, Dec 30 2012
Comments