A295733 a(n) = a(n-1) + 3*a(n-2) -2*a(n-3) - 2*a(n-4), where a(0) = 0, a(1) = -1, a(2) = -1, a(3) = 1.

0, -1, -1, 1, 0, 7, 7, 26, 33, 83, 116, 247, 363, 706, 1069, 1967, 3036, 5387, 8423, 14578, 23001, 39115, 62116, 104303, 166419, 276866, 443285, 732439, 1175724, 1932739, 3108463, 5090354, 8198817, 13387475, 21586292, 35170375, 56756667, 92320258, 149076925

Offset

0,6

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) = 0; a(1) = -1, a(2) = -1, a(3) = 1.

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

Mathematica

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

Crossrefs

Cf. A001622, A000045, A005672.

Sequence in context: A247666 A255279 A230496 * A341201 A255277 A027844

Adjacent sequences: A295730 A295731 A295732 * A295734 A295735 A295736

Keyword

easy,sign

Author

Clark Kimberling, Nov 30 2017

Status

approved