

A295850


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


1



0, 0, 2, 1, 7, 6, 21, 23, 60, 75, 167, 226, 457, 651, 1236, 1823, 3315, 5010, 8837, 13591, 23452, 36531, 62031, 97538, 163665, 259155, 431012, 686071, 1133467, 1811346, 2977581, 4772543, 7815660, 12555435, 20502167, 32992066, 53756377, 86617371, 140898036
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OFFSET

0,3


COMMENTS

a(n)/a(n1) > (1 + sqrt(5))/2 = golden ratio (A001622), so that a( ) has the growth rate of the Fibonacci numbers (A000045).
Therefore the terms are all >= 0.  Georg Fischer, Feb 19 2019


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(n1) + 3*a(n2)  2*a(n3)  2*a(n4), where a(0) = 0, a(1) = 0, a(2) = 2, a(3) = 1. [Corrected by Colin Barker, Dec 15 2017]
G.f.: (((2 + x) x^2)/((1 + x + x^2) (1 + 2 x^2))).
From Colin Barker, Dec 15 2017: (Start)
a(n) = 2^((n3)/2+3/2) + ((1sqrt(5))/2)^(n+1) + (2/(1+sqrt(5)))^(n1) for n even.
a(n) = 3*2^((n3)/2+1) + ((1sqrt(5))/2)^(n+1) + (2/(1+sqrt(5)))^(n1) for n odd.
(End)


MATHEMATICA

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


CROSSREFS

Cf. A001622, A000045.
Sequence in context: A257577 A060583 A246751 * A078104 A072280 A217106
Adjacent sequences: A295847 A295848 A295849 * A295851 A295852 A295853


KEYWORD

easy,nonn


AUTHOR

Clark Kimberling, Dec 01 2017


STATUS

approved



