A278764 Pisot sequence T(5,13).
5, 13, 33, 83, 208, 521, 1305, 3268, 8183, 20490, 51306, 128467, 321673, 805448, 2016788, 5049902, 12644616, 31661270, 79277695, 198506027, 497045767, 1244569236, 3116317824, 7803050645, 19538315026, 48922629292, 122498979756, 306729222415, 768029383352, 1923094020999, 4815298338536
Offset: 0
Crossrefs
Programs
-
Mathematica
RecurrenceTable[{a[0] == 5, a[1] == 13, a[n] == Floor[a[n - 1]^2/a[n - 2]]}, a, {n, 30}]
Formula
a(n) = floor(a(n-1)^2/a(n-2)), a(0) = 5, a(1) = 13.
Conjectures: (Start)
G.f.: (5 - 2*x + 4*x^2 - 5*x^3 + x^4 - 2*x^5)/((1 - x)*(1 - 2*x - 3*x^3 - x^5)).
a(n) = 3*a(n-1) - 2*a(n-2) + 3*a(n-3) - 3*a(n-4) + a(n-5) - a(n-6). (End)