

A289521


Number of vertices in a planar Apollonian graph at iteration n.


7



4, 7, 16, 43, 124, 367, 1096, 3283, 9844, 29527, 88576, 265723, 797164, 2391487, 7174456, 21523363, 64570084, 193710247, 581130736, 1743392203, 5230176604, 15690529807, 47071589416, 141214768243, 423644304724, 1270932914167, 3812798742496, 11438396227483, 34315188682444
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OFFSET

1,1


LINKS



FORMULA

G.f.: x*(4  9*x) / ((1  x)*(1  3*x)).
a(n) = (5 + 3^n) / 2.
a(n) = 4*a(n1)  3*a(n2) for n>2.
(End)


PROG

(PARI) Vec(x*(4  9*x) / ((1  x)*(1  3*x)) + O(x^30)) \\ Colin Barker, Jul 07 2017


CROSSREFS



KEYWORD

nonn,easy


AUTHOR



STATUS

approved



