A295725 a(n) = a(n-1) + 3*a(n-2) -2*a(n-3) - 2*a(n-4), where a(0) = 0, a(1) = 0, a(2) = -1, a(3) = 1.

0, 0, -1, 1, -2, 3, -3, 8, -3, 21, 2, 55, 25, 144, 105, 377, 354, 987, 1085, 2584, 3157, 6765, 8898, 17711, 24561, 46368, 66833, 121393, 180034, 317811, 481461, 832040, 1280733, 2178309, 3393506, 5702887, 8965321, 14930352, 23633529, 39088169, 62197410

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, 0, -1, 1}, 100]

Formula

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

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