A295857 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) = 2, a(3) = 3.

0, 0, 2, 3, 9, 14, 31, 49, 96, 153, 281, 450, 795, 1277, 2200, 3541, 5997, 9666, 16175, 26097, 43296, 69905, 115249, 186178, 305523, 493749, 807464, 1305309, 2129157, 3442658, 5604583, 9063625, 14733744, 23830137, 38694953, 62590626, 101547723, 164269421

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) = 0, a(2) = 2, a(3) = 3.

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

Mathematica

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

Crossrefs

Cf. A001622, A000045.

Sequence in context: A113501 A101067 A056645 * A047171 A094557 A222658

Adjacent sequences: A295854 A295855 A295856 * A295858 A295859 A295860

Keyword

nonn,easy

Author

Clark Kimberling, Dec 01 2017

Status

approved