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.

-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

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

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

Cf. A001622, A000045.

Sequence in context: A340740 A306707 A180958 * A230630 A343957 A338505

Adjacent sequences: A295851 A295852 A295853 * A295855 A295856 A295857

Keyword

easy,sign

Author

Clark Kimberling, Dec 01 2017

Status

approved