The OEIS is supported by the many generous donors to the OEIS Foundation.

 Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 60th year, we have over 367,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”). Other ways to Give
 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 LINKS Colin Barker, Table of n, a(n) for n = 1..1000 Eric Weisstein's World of Mathematics, Apollonian Network Index entries for linear recurrences with constant coefficients, signature (4,-3). 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 Adjacent sequences: A289518 A289519 A289520 * A289522 A289523 A289524 KEYWORD nonn,easy AUTHOR Andrew D. Walker, Jul 07 2017 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified December 4 15:16 EST 2023. Contains 367563 sequences. (Running on oeis4.)