A247308 - OEIS

%I #38 Oct 15 2022 03:36:03

%S 1,7,37,163,661,2643,10497,41511,164073,648495,2562749,10127291,

%T 40020845,158152811,624980489,2469769903,9759926065,38568829879,

%U 152414547541,602304889075,2380161078405,9405812345187,37169461719153,146884589311479,580451843386809,2293803210617951,9064547264192237,35820865853787467

%N Layer counting sequence in the order-5 cubic honeycomb.

%C The number of cubes reachable by at most n steps across faces in the {4,3,5} tessellation of hyperbolic space, for n >= 0.

%H Eryk Kopczynski, <a href="/A247308/b247308.txt">Table of n, a(n) for n = 0..999</a>

%H Tim Hutton, <a href="https://code.google.com/p/reaction-diffusion/source/browse/trunk/Ready/src/readybase/MeshGenerators.cpp?spec=svn1325&amp;r=1325#949">Generating code in C++, using VTK</a> (gives incorrect terms from some point on!)

%H Eryk Kopczynski, <a href="https://github.com/zenorogue/hyperrogue/">HyperRogue</a>. Run with parameters -geo 435h -csolve; compile with -DCAP_GMP=0 to get the conjectured formula.

%F a(d+17) = 3*a(d+16) + 2*a(d+15) + 7*a(d+14) + a(d+13) - 5*a(d+12) + 3*a(d+11) - 2*a(d+10) - 18*a(d+9) + 18*a(d+8) + 2*a(d+7) - 3*a(d+6) + 5*a(d+5) - a(d+4) - 7*a(d+3) - 2*a(d+2) - 3*a(d+1) + a(d) (conjectured, found experimentally and tested from 19 to 135). - _Eryk Kopczynski_, Jul 04 2020

%Y For the {5,3,4} tessellation: A076765.

%Y For the {5,4} tessellation: A054888.

%K nonn

%O 0,2

%A _Tim Hutton_, Sep 11 2014

%E Offset and terms corrected and more terms added by _Eryk Kopczynski_, Jul 04 2020