A295728 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, 4, 7, 15, 26, 49, 83, 148, 247, 427, 706, 1197, 1967, 3292, 5387, 8935, 14578, 24025, 39115, 64164, 104303, 170515, 276866, 451477, 732439, 1192108, 1932739, 3141231, 5090354, 8264353, 13387475, 21717364, 35170375, 57018811, 92320258, 149601213

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).

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) = 1, a(1) = -1, a(2) = 1, a(3) = 1.

G.f.: (1 - 2 x - x^2 + 5 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

Cf. A001622, A000045, A005672.

Sequence in context: A269967 A124286 A235603 * A027419 A301204 A116969

Adjacent sequences: A295725 A295726 A295727 * A295729 A295730 A295731

Keyword

easy,sign

Author

Clark Kimberling, Nov 29 2017

Status

approved