OFFSET
0,2
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..1000
Amir Sapir, The Tower of Hanoi with Forbidden Moves, The Computer J. 47 (1) (2004) 20, case cyclic++, sequence c(n) (offset 1).
Index entries for linear recurrences with constant coefficients, signature (2,3,-4).
FORMULA
G.f.: (1+x)/((1-x)*(1-x-4*x^2)). - Ralf Stephan, Feb 04 2004
From Klaus Purath, Feb 02 2021: (Start)
a(n) = 2*a(n-1) + 3*a(n-2) - 4*a(n-3).
a(n) = Sum_{j=0..n} A026597(j). (End)
a(n) = 2^n*(Fibonacci(n+2, 1/2) + Fibonacci(n+1, 1/2)) - 1/2. - G. C. Greubel, Dec 15 2021
MATHEMATICA
LinearRecurrence[{2, 3, -4}, {1, 3, 9}, 40] (* G. C. Greubel, Dec 15 2021 *)
PROG
(Magma) [n le 3 select 3^(n-1) else 2*Self(n-1) +3*Self(n-2) -4*Self(n-3): n in [1..41]]; // G. C. Greubel, Dec 15 2021
(Sage) [( (1+x)/((1-x)*(1-x-4*x^2)) ).series(x, n+1).list()[n] for n in (0..40)] # G. C. Greubel, Dec 15 2021
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
STATUS
approved