

A295853


a(n) = a(n1) + 3*a(n2) 2*a(n3)  2*a(n4), where a(0) = 2, a(1) = 1, a(2) = 2, a(3) = 1.


1



2, 1, 2, 1, 13, 14, 47, 61, 148, 209, 437, 646, 1243, 1889, 3452, 5341, 9433, 14774, 25487, 40261, 68308, 108569, 181997, 290566, 482803, 773369, 1276652, 2050021, 3367633, 5417654, 8867207, 14284861, 23315908, 37600769, 61244357, 98845126, 160744843
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OFFSET

0,1


COMMENTS

a(n)/a(n1) > (1 + sqrt(5))/2 = golden ratio (A001622), so that a( ) has the growth rate of the Fibonacci numbers (A000045).


LINKS



FORMULA

a(n) = a(n1) + a(n3) + a(n4), where a(0) = 2, a(1) = 1, a(2) = 2, a(3) = 1.
G.f.: (2 + x + 9 x^2  2 x^3)/(1  x  3 x^2 + 2 x^3 + 2 x^4).


MATHEMATICA

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


CROSSREFS



KEYWORD

easy,sign


AUTHOR



STATUS

approved



