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A295854 a(n) = a(n-1) + 3*a(n-2) -2*a(n-3) - 2*a(n-4), where a(0) = -2, a(1) = -2, a(2) = 2, a(3) = 1. 1
-2, -2, 2, 1, 15, 18, 57, 79, 184, 271, 551, 838, 1581, 2451, 4416, 6931, 12115, 19174, 32825, 52255, 88152, 140919, 235215, 377158, 624661, 1003867, 1653104, 2661067, 4363323, 7032582, 11494209, 18543175, 30233992, 48809935, 79437143, 128312614, 208536189 (list; graph; refs; listen; history; text; internal format)
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).
LINKS
FORMULA
a(n) = a(n-1) + a(n-3) + a(n-4), where a(0) = -2, a(1) = -2, a(2) = 2, a(3) = 1.
G.f.: (-2 + 10 x^2 + x^3)/(1 - x - 3 x^2 + 2 x^3 + 2 x^4).
MATHEMATICA
LinearRecurrence[{1, 3, -2, -2}, {-2, -2, 2, 1}, 100]
CoefficientList[Series[(x^3+10*x^2-2)/(2*x^4+2*x^3-3*x^2-x+1), {x, 0, 40}], x] (* Harvey P. Dale, Mar 05 2018 *)
CROSSREFS
Sequence in context: A340740 A306707 A180958 * A230630 A343957 A338505
KEYWORD
easy,sign
AUTHOR
Clark Kimberling, Dec 01 2017
STATUS
approved

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Last modified July 24 22:37 EDT 2024. Contains 374585 sequences. (Running on oeis4.)