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A247308 Layer counting sequence in the order-5 cubic honeycomb.

%I A247308 #52 Jun 02 2025 16:49:53
%S A247308 1,7,37,163,661,2643,10497,41511,164073,648495,2562749,10127291,
%T A247308 40020845,158152811,624980489,2469769903,9759926065,38568829879,
%U A247308 152414547541,602304889075,2380161078405,9405812345187,37169461719153,146884589311479,580451843386809,2293803210617951,9064547264192237,35820865853787467
%N A247308 Layer counting sequence in the order-5 cubic honeycomb.
%C A247308 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 A247308 Eryk Kopczynski, <a href="/A247308/b247308.txt">Table of n, a(n) for n = 0..999</a>
%H A247308 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 A247308 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 A247308 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
%F A247308 Conjectured G.f.: (1+x) * (1+2*x+8*x^2+9*x^3+8*x^4+17*x^5+10*x^6+10*x^8+10*x^10+17*x^11+8*x^12+9*x^13+8*x^14+2*x^15+x^16) / ((1-x)^2 * (1-2*x-4*x^2-11*x^3-12*x^4-7*x^5-10*x^6-8*x^7+10*x^8-8*x^9-10*x^10-7*x^11-12*x^12-11*x^13-4*x^14-2*x^15+x^16)). - _Natalia L. Skirrow_, Apr 29 2025
%Y A247308 For the {5,3,4} tessellation: A076765.
%Y A247308 For the {5,4} tessellation: A054888.
%K A247308 nonn
%O A247308 0,2
%A A247308 _Tim Hutton_, Sep 11 2014
%E A247308 Offset and terms corrected and more terms added by _Eryk Kopczynski_, Jul 04 2020