The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A299285 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A299285

Coordination sequence for "tea" 3D uniform tiling.
(history; published version)

#25 by N. J. A. Sloane at Wed Jun 12 17:15:16 EDT 2024

STATUS

editing

approved

#24 by N. J. A. Sloane at Wed Jun 12 17:15:04 EDT 2024

FORMULA

[I suspect Barker's formulas only conjectures. - N. J. A. Sloane, Jun 12 2024]

If the above formulas are true, then a(n) = (31 - 3*(-1)^n + 126*n^2 + 4*A056594(n))/16 for n > 0. - Stefano Spezia, Jun 08 2024

STATUS

proposed

editing

#23 by Michel Marcus at Tue Jun 11 04:02:46 EDT 2024

STATUS

editing

proposed

#22 by Michel Marcus at Tue Jun 11 04:02:42 EDT 2024

REFERENCES

B. Grünbaum, Uniform tilings of 3-space, Geombinatorics, 4 (1994), 49-56. See tiling #4.

LINKS

B. Grünbaum, <a href="https://faculty.washington.edu/moishe/branko/BG199.Uniform%20Tilings%20of%203-Space.pdf">Uniform tilings of 3-space</a>, Geombinatorics, 4 (1994), 49-56. See tiling #4.

STATUS

proposed

editing

#21 by Stefano Spezia at Sat Jun 08 06:57:48 EDT 2024

STATUS

editing

proposed

#20 by Stefano Spezia at Sat Jun 08 04:40:26 EDT 2024

CROSSREFS

Cf. A056594.

#19 by Stefano Spezia at Sat Jun 08 04:33:10 EDT 2024

FORMULA

Conjectures from _From _Colin Barker_, Feb 11 2018: (Start)

Conjecture: a(n) = (31 - 3*(-1)^n + 126*n^2 + 4*A056594(n))/16 for n > 0. - Stefano Spezia, Jun 08 2024

Discussion

Sat Jun 08

04:34

Stefano Spezia: From Harvey and Charles code, I guess that Colin conjectures are true. I derived new formula from Colin g.f.

#18 by Stefano Spezia at Sat Jun 08 04:31:49 EDT 2024

FORMULA

a(n) = 2*a(n-1) - a(n-2) + a(n-4) - 2*a(n-5) + a(n-6) for n>6. (End)

(End)

Conjecture: a(n) = (31 - 3*(-1)^n + 126*n^2 + 4*A056594(n))/16 for n > 0. - Stefano Spezia, Jun 08 2024

STATUS

approved

editing

#17 by Charles R Greathouse IV at Tue Oct 18 14:45:50 EDT 2022

STATUS

editing

approved

#16 by Charles R Greathouse IV at Tue Oct 18 14:45:48 EDT 2022

PROG

(PARI) a(n)=([0, 1, 0, 0, 0, 0; 0, 0, 1, 0, 0, 0; 0, 0, 0, 1, 0, 0; 0, 0, 0, 0, 1, 0; 0, 0, 0, 0, 0, 1; 1, -2, 1, 0, -1, 2]^n*[1; 10; 33; 73; 128; 199])[1, 1] \\ Charles R Greathouse IV, Oct 18 2022

KEYWORD

nonn,easy

STATUS

approved

editing