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A295684
a(n) = a(n-1) + a(n-3) + a(n-4), where a(0) = 2, a(1) = 0, a(2) = 1, a(3) = 1.
1
2, 0, 1, 1, 3, 4, 6, 10, 17, 27, 43, 70, 114, 184, 297, 481, 779, 1260, 2038, 3298, 5337, 8635, 13971, 22606, 36578, 59184, 95761, 154945, 250707, 405652, 656358, 1062010, 1718369, 2780379, 4498747, 7279126, 11777874, 19057000, 30834873, 49891873, 80726747
OFFSET
0,1
COMMENTS
a(n)/a(n-1) -> (1 + sqrt(5))/2 = golden ratio (A001622), so that a( ) has the growth rate of the Fibonacci numbers (A000045).
FORMULA
a(n) = a(n-1) + a(n-3) + a(n-4), where a(0) = 2, a(1) = 0, a(2) = 1, a(3) = 1.
G.f.: (-2 + 2 x - x^2 + 2 x^3)/(-1 + x + x^3 + x^4).
MATHEMATICA
LinearRecurrence[{1, 0, 1, 1}, {2, 0, 1, 1}, 100]
CROSSREFS
Sequence in context: A354668 A215086 A261440 * A276890 A276921 A339677
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, Nov 29 2017
STATUS
approved