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A295855 a(n) = a(n-1) + 3*a(n-2) -2*a(n-3) - 2*a(n-4), where a(0) = 1, a(1) = -2, a(2) = 2, a(3) = 1. 1
1, -2, 2, 1, 9, 12, 33, 49, 106, 163, 317, 496, 909, 1437, 2538, 4039, 6961, 11128, 18857, 30241, 50634, 81387, 135093, 217504, 358741, 578293, 949322, 1531711, 2505609, 4045512, 6600273, 10662169, 17360746, 28055683, 45613037, 73734256, 119740509, 193605837 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
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).
LINKS
FORMULA
a(n) = a(n-1) + a(n-3) + a(n-4), where a(0) = 1, a(1) = -2, a(2) = 2, a(3) = 1.
G.f.: (1 - 3 x + x^2 + 7 x^3)/(1 - x - 3 x^2 + 2 x^3 + 2 x^4).
MATHEMATICA
LinearRecurrence[{1, 3, -2, -2}, {1, -2, 2, 1}, 100]
CROSSREFS
Sequence in context: A136730 A175714 A291082 * A364371 A285068 A306149
KEYWORD
easy,sign
AUTHOR
Clark Kimberling, Dec 01 2017
STATUS
approved

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Last modified July 24 05:58 EDT 2024. Contains 374575 sequences. (Running on oeis4.)