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A295860 a(n) = a(n-1) + 3*a(n-2) -2*a(n-3) - 2*a(n-4), where a(0) = -2, a(1) = 1, a(2) = 0, a(3) = 1. 5
-2, 1, 0, 1, 3, 4, 11, 15, 34, 49, 99, 148, 279, 427, 770, 1197, 2095, 3292, 5643, 8935, 15090, 24025, 40139, 64164, 106351, 170515, 280962, 451477, 740631, 1192108, 1949123, 3141231, 5123122, 8264353, 13453011, 21717364, 35301447, 57018811, 92582402 (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

Clark Kimberling, Table of n, a(n) for n = 0..2000

Index entries for linear recurrences with constant coefficients, signature (1,3,-2,-2)

FORMULA

G.f.: (-2 + 3 x + 5 x^2 - 6 x^3)/(1 - x - 3 x^2 + 2 x^3 + 2 x^4).

a(n) = -A016116(n+1) + 4*A000045(n) - A000045(n+1). - Robert Israel, Jan 12 2018

MAPLE

f:= n -> - 2^floor((n+1)/2) + 4*combinat:-fibonacci(n) - combinat:-fibonacci(n+1):

map(f, [$0..30]); # Robert Israel, Jan 12 2018

MATHEMATICA

LinearRecurrence[{1, 3, -2, -2}, {-2, 1, 0, 1}, 100]

CROSSREFS

Cf. A001622, A000045, A016116.

Sequence in context: A214075 A322267 A286933 * A118345 A292804 A118350

Adjacent sequences:  A295857 A295858 A295859 * A295861 A295862 A295863

KEYWORD

easy,sign

AUTHOR

Clark Kimberling, Jan 07 2018

STATUS

approved

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Last modified May 22 19:19 EDT 2019. Contains 323481 sequences. (Running on oeis4.)