A295720 a(n) = a(n-1) + 3*a(n-2) -2*a(n-3) - 2*a(n-4), where a(0) = 1, a(1) = 4, a(2) = 9, a(3) = 16.

1, 4, 9, 16, 33, 55, 104, 171, 307, 502, 873, 1423, 2424, 3943, 6623, 10758, 17893, 29035, 47952, 77755, 127755, 207046, 338897, 549015, 896104, 1451263, 2363751, 3827302, 6223821, 10075699, 16365056, 26489907, 42986035, 69574246, 112822425, 182593279

Offset: 0

Author

Clark Kimberling, Nov 29 2017

Keywords

• nonn
• easy

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, 4, 9, 16}, 100]

Formula

a(n) = a(n-1) + a(n-3) + a(n-4), where a(0) = 1, a(1) = 4, a(2) = 9, a(3) = 16.

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