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A295732
a(n) = a(n-1) + 3*a(n-2) -2*a(n-3) - 2*a(n-4), where a(0) = -1, a(1) = -1, a(2) = -1, a(3) = 1.
1
-1, -1, -1, 1, 2, 9, 15, 36, 59, 119, 194, 361, 587, 1044, 1695, 2931, 4754, 8069, 13079, 21916, 35507, 58959, 95490, 157521, 255059, 418724, 677879, 1108891, 1794962, 2928429, 4739775, 7717356, 12489899, 20305559, 32860994, 53363161, 86355227, 140111604
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) = -1, a(2) = -1, a(3) = 1.
G.f.: (-1 + 3 x^2 + 3 x^3)/(1 - x - 3 x^2 + 2 x^3 + 2 x^4).
MATHEMATICA
LinearRecurrence[{1, 3, -2, -2}, {-1, -1, -1, 1}, 100]
CROSSREFS
KEYWORD
easy,sign
AUTHOR
Clark Kimberling, Nov 30 2017
STATUS
approved