A295732 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, 2, 9, 15, 36, 59, 119, 194, 361, 587, 1044, 1695, 2931, 4754, 8069, 13079, 21916, 35507, 58959, 95490, 157521, 255059, 418724, 677879, 1108891, 1794962, 2928429, 4739775, 7717356, 12489899, 20305559, 32860994, 53363161, 86355227, 140111604

Offset: 0

Author

Clark Kimberling, Nov 30 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}, {-1, -1, -1, 1}, 100]

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