OFFSET
0,1
COMMENTS
From Johannes W. Meijer, Aug 14 2010: (Start)
The sequence b(n+1)=2*a(n), n>= 0 with b(0)=1, is a berserker sequence, see A180141. For the corner squares 16 A[5] vectors, with decimal values between 19 and 400, lead to the b(n) sequence.
(End)
Not to be confused with the Pisot T(2,8) sequence, which is A004171. - R. J. Mathar, Feb 13 2016
LINKS
Colin Barker, 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 linear recurrences with constant coefficients, signature (4,0,-2).
FORMULA
From Johannes W. Meijer, Aug 14 2010: (Start)
G.f.: (2-x^2)/(1-4*x+2*x^3).
a(n) = 4*a(n-1)-2*a(n-3) with a(0)=2, a(1)=8 and a(2)=31.
a(n) = (119-24*z1-64*z1^2)*z1^(-n-1)/202+(119-24*z2-64*z2^2)*z2^(-n-1)/202+(119-24*z3-64*z3^2)*z3^(-n-1)/202 with alpha=2*arctan(sqrt(303)/9), p=(sqrt(6)/3)*sin((alpha+Pi)/6), q=sqrt(2)*cos((alpha+Pi)/6), z1:=2*p, z2=(-q-p) and z3=(q-p).
(End)
MATHEMATICA
LinearRecurrence[{4, 0, -2}, {2, 8, 31}, 25] (* Vincenzo Librandi, Feb 15 2016 *)
PROG
(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(2, 8, 30) \\ Colin Barker, Feb 14 2016
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
EXTENSIONS
More terms from Johannes W. Meijer, Aug 14 2010
STATUS
approved