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

1,1

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

Table of n, a(n) for n=1..44.

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).

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

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 *)

Crossrefs

Sequence in context: A152507 A203100 A351678 * A377417 A273000 A282328

Adjacent sequences: A378452 A378453 A378454 * A378456 A378457 A378458

Keyword

nonn,easy

Author

Craig Knecht, Nov 26 2024

Status

approved