bibkey: mathar2010a178294
authors: Richard J. Mathar
year: 2010
title: "OEIS A178294, Number of collinear point triples in a 4 X 4 X 4 X... n-dimensional cubic grid"
doi: null
url: https://oeis.org/A178294
claim: "%N A178294 Number of collinear point triples in a 4 X 4 X 4 X... n-dimensional cubic grid. %A A178294 _R. H. Hardin_, suggested by R. J. Mathar in the Sequence Fans Mailing List, May 24 2010 %F A178294 Conjecture: a(n) = 8^n/2-3*4^n/2+6^n. - _R. J. Mathar_, May 24 2010"
strata_touched:
  - D5/S3/Arith/Lattices/FourGridCollinearTriples
license: citation-only
triage: anchor

OEIS A178294

The entry counts unordered collinear triples in the Cartesian power of a four-point grid. R. H. Hardin submitted the sequence after R. J. Mathar suggested it on the Sequence Fans Mailing List on May 24, 2010. The same entry attributes the conjectural closed form to Mathar on that date.

Mathar’s attached note a178294.pdf, Points on a line in the finite d-dimensional simple cubic lattice, is the source of the conjectural calculation. The recurrence and generating function printed later on the FORMULA line follow algebraically from the displayed closed form.

Verified locator

• URL: https://oeis.org/A178294
• Locator: FORMULA (verbatim): Conjecture: a(n) = 8^n/2-34^n/2+6^n. a(n) = +18a(n-1) -104a(n-2) +192a(n-3). G.f.: 4x(-1+7x)/((6x-1)(8x-1)(4x-1)). - R. J. Mathar, May 24 2010