A295851 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) = 2, a(3) = 1.

0, -1, 2, 1, 9, 10, 31, 41, 96, 137, 281, 418, 795, 1213, 2200, 3413, 5997, 9410, 16175, 25585, 43296, 68881, 115249, 184130, 305523, 489653, 807464, 1297117, 2129157, 3426274, 5604583, 9030857, 14733744, 23764601, 38694953, 62459554, 101547723, 164007277

Offset

0,3

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) = 2, a(3) = 1.

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

Mathematica

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

Crossrefs

Cf. A001622, A000045.

Sequence in context: A059604 A048160 A305178 * A368375 A192324 A063579

Adjacent sequences: A295848 A295849 A295850 * A295852 A295853 A295854

Keyword

easy,sign

Author

Clark Kimberling, Dec 01 2017

Status

approved