OFFSET
1,6
LINKS
G. C. Greubel, Table of n, a(n) for n = 1..500
Index entries for linear recurrences with constant coefficients, signature (4,-3,-3,0,3,2).
FORMULA
a(n) = 2^n - 2*(tribonacci(n+3) - Fibonacci(n+1)), where tribonacci = A000073.
From R. J. Mathar, Feb 06 2010: (Start)
a(n) = 4*a(n-1) - 3*a(n-2) - 3*a(n-3) + 3*a(n-5) + 2*a(n-6).
G.f.: -2*x^6/((2*x-1)*(x^2+x-1)*(x^3+x^2+x-1)). (End)
MATHEMATICA
b[1] = 0; b[2] = 1; b[3] = 1; b[n_]: = b[n-1] + b[n-2] + b[n-3]; Table[2^n - 2*(Sum[b[n + 3 - i], {i, 1, 3}] - Fibonacci[n + 1]), {n, 1, 30}]
LinearRecurrence[{4, -3, -3, 0, 3, 2}, {0, 0, 0, 0, 0, 2}, 50] (* G. C. Greubel, Jun 27 2016 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
V.J. Pohjola, Nov 13 2009
STATUS
approved