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