A295856 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) = 3, a(3) = 1.

0, 0, 3, 1, 10, 7, 29, 28, 81, 93, 222, 283, 601, 820, 1613, 2305, 4302, 6351, 11421, 17260, 30217, 46453, 79742, 124147, 210033, 330084, 552405, 874297, 1451278, 2309191, 3809621, 6086044, 9993969, 16014477, 26205054, 42088459, 68686729, 110513044

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) = 3, a(3) = 1.

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

Mathematica

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

Crossrefs

Cf. A001622, A000045.

Sequence in context: A046658 A124574 A322383 * A052964 A084178 A262030

Adjacent sequences: A295853 A295854 A295855 * A295857 A295858 A295859

Keyword

nonn,easy

Author

Clark Kimberling, Dec 01 2017

Status

approved