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A247308 Layer counting sequence in the order-5 cubic honeycomb. 1
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 (list; graph; refs; listen; history; text; internal format)
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=0,1,2...

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

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Last modified June 16 21:55 EDT 2021. Contains 345080 sequences. (Running on oeis4.)