A295726 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, 6, 9, 23, 36, 75, 119, 226, 361, 651, 1044, 1823, 2931, 5010, 8069, 13591, 21916, 36531, 58959, 97538, 157521, 259155, 418724, 686071, 1108891, 1811346, 2928429, 4772543, 7717356, 12555435, 20305559, 32992066, 53363161, 86617371, 140111604

Offset: 0

Author

Clark Kimberling, Nov 29 2017

Keywords

• easy
• sign

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)

Crossrefs

Cf. A001622, A000045, A005672.

Programs

Mathematica

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

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 + 2 x^2 + 3 x^3)/(1 - x - 3 x^2 + 2 x^3 + 2 x^4).