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A295719 a(n) = a(n-1) + 3*a(n-2) -2*a(n-3) - 2*a(n-4), where a(0) = 1, a(1) = 3, a(2) = 6, a(3) = 10. 1
1, 3, 6, 10, 20, 32, 60, 96, 172, 276, 480, 772, 1316, 2120, 3564, 5748, 9568, 15444, 25524, 41224, 67772, 109508, 179328, 289860, 473284, 765192, 1246668, 2015956, 3279008, 5303156, 8614932, 13934472, 22614940, 36582180, 59328192, 95975908, 155566244 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

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) = 1, a(1) = 3, a(2) = 6, a(3) = 10.

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

MATHEMATICA

LinearRecurrence[{1, 3, -2, -2}, {1, 3, 6, 10}, 100]

CROSSREFS

Cf. A001622, A000045, A005672.

Sequence in context: A183324 A058356 A270048 * A178850 A018171 A306357

Adjacent sequences:  A295716 A295717 A295718 * A295720 A295721 A295722

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling, Nov 29 2017

STATUS

approved

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Last modified December 1 10:36 EST 2021. Contains 349427 sequences. (Running on oeis4.)