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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
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).
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
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, Nov 29 2017
STATUS
approved