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

1, 7, 37, 163, 661, 2643, 10497, 41511, 164073, 648495, 2562749, 10127291, 40020845, 158152811, 624980489, 2469769903, 9759926065, 38568829879, 152414547541, 602304889075, 2380161078405, 9405812345187, 37169461719153, 146884589311479, 580451843386809, 2293803210617951, 9064547264192237, 35820865853787467

Offset

0,2

Comments

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

Links

Eryk Kopczynski, Table of n, a(n) for n = 0..999

Tim Hutton, Generating code in C++, using VTK (gives incorrect terms from some point on!)

Eryk Kopczynski, HyperRogue. Run with parameters -geo 435h -csolve; compile with -DCAP_GMP=0 to get the conjectured formula.

Formula

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

Crossrefs

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

For the {5,4} tessellation: A054888.

Sequence in context: A201962 A269257 A269258 * A175284 A049494 A049495

Adjacent sequences: A247305 A247306 A247307 * A247309 A247310 A247311

Keyword

nonn

Author

Tim Hutton, Sep 11 2014

Extensions

Offset and terms corrected and more terms added by Eryk Kopczynski, Jul 04 2020

Status

approved