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A295729
a(n) = a(n-1) + 3*a(n-2) -2*a(n-3) - 2*a(n-4), where a(0) = -1, a(1) = 0, a(2) = 1, a(3) = 1.
1
-1, 0, 1, 1, 6, 7, 21, 28, 65, 93, 190, 283, 537, 820, 1485, 2305, 4046, 6351, 10909, 17260, 29193, 46453, 77694, 124147, 205937, 330084, 544213, 874297, 1434894, 2309191, 3776853, 6086044, 9928433, 16014477, 26073982, 42088459, 68424585, 110513044
OFFSET
0,5
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) = -1, a(1) = 0, a(2) = 1, a(3) = 1.
G.f.: (-1 + x + 4 x^2 - 2 x^3)/(1 - x - 3 x^2 + 2 x^3 + 2 x^4).
MATHEMATICA
LinearRecurrence[{1, 3, -2, -2}, {-1, 0, 1, 1}, 100]
CROSSREFS
KEYWORD
easy,sign
AUTHOR
Clark Kimberling, Nov 30 2017
STATUS
approved