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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
OFFSET
1,1
LINKS
Eric Weisstein's World of Mathematics, Apollonian Network
FORMULA
From Colin Barker, Jul 07 2017: (Start)
G.f.: x*(4 - 9*x) / ((1 - x)*(1 - 3*x)).
a(n) = (5 + 3^n) / 2.
a(n) = 4*a(n-1) - 3*a(n-2) for n>2.
(End)
a(n) = a(n-1) + 3^(n-1) for n>1. - Andrew D. Walker, Jul 07 2017
PROG
(PARI) a(n)=(3^n+5)/2 \\ Charles R Greathouse IV, Jul 07 2017
(PARI) Vec(x*(4 - 9*x) / ((1 - x)*(1 - 3*x)) + O(x^30)) \\ Colin Barker, Jul 07 2017
CROSSREFS
Sequence in context: A050357 A296059 A132334 * A097661 A182561 A246915
KEYWORD
nonn,easy
AUTHOR
Andrew D. Walker, Jul 07 2017
STATUS
approved