A378455 Total number of coronal tilings of a width one length n straight polyiamond central frame with a specific hexiamond tile.

1272, 2644, 2684, 3141, 3144, 3185, 3184, 3185, 3184, 3185, 3184, 3185, 3184, 3185, 3184, 3185, 3184, 3185, 3184, 3185, 3184, 3185, 3184, 3185, 3184, 3185, 3184, 3185, 3184, 3185, 3184, 3185, 3184, 3185, 3184, 3185, 3184, 3185, 3184, 3185, 3184, 3185, 3184, 3185

Offset: 1

Author

Craig Knecht, Nov 26 2024

Keywords

• nonn
• easy

Comments

For even length n>4 the total number of coronal tilings is 3185.

For odd length n>5 the total number of coronal tilings is 3184.

The corona can be composed of different numbers of coronal tiles. The number of coronal tilings for a given number of coronal tiles is noted.

Links

• Craig Knecht, Coronal detail.
• Craig Knecht, Example for the sequence.
• Craig Knecht, n=9, 16 coronal tiles, 72 tilings.
• Craig Knecht, Repeating 3185 3184 coronal tiling totals.
• Index entries for linear recurrences with constant coefficients, signature (0,1).

Programs

Mathematica

Drop[CoefficientList[Series[x*(1272 + 2644*x + 1412*x^2 + 497*x^3 + 460*x^4 + 44*x^5 + 40*x^6)/(1 - x^2), {x,0,32}], x], 1] (* Georg Fischer, Feb 11 2025 *)

Formula

G.f.: x*(1272 + 2644*x + 1412*x^2 + 497*x^3 + 460*x^4 + 44*x^5 + 40*x^6)/(1 - x^2). - Stefano Spezia, Nov 27 2024