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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. 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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified September 20 19:05 EDT 2019. Contains 327246 sequences. (Running on oeis4.)