OFFSET
0,2
COMMENTS
lim_{n -> infinity} a(n)/a(n-1) = 16.
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..200
Index entries for linear recurrences with constant coefficients, signature (21,-84,64).
FORMULA
a(n) = (257*16^n - 85*4^n + 8)/180.
G.f.: (1+x^2)/((1-x)*(1-4*x)*(1-16*x)).
From G. C. Greubel, May 30 2016: (Start)
a(n) = 21*a(n-1) - 84*a(n-2) + 64*a(n-3) for n>2.
E.g.f.: (1/180)*(257*exp(16*x) - 85*exp(4*x) + 8*exp(x)). (End)
MAPLE
MATHEMATICA
LinearRecurrence[{21, -84, 64}, {1, 21, 358}, 50] (* G. C. Greubel, May 30 2016 *)
RecurrenceTable[{a[0]==1, a[1]==21, a[n]==20a[n-1]-64a[n-2]+2}, a, {n, 20}] (* Harvey P. Dale, Oct 27 2019 *)
PROG
(Magma) [ n le 2 select 20*n-19 else 20*Self(n-1)-64*Self(n-2)+2: n in [1..17] ];
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Klaus Brockhaus, Oct 27 2009
STATUS
approved