A317541 -id:A317541

Search: a317541 -id:a317541

Displaying 1-2 of 2 results found.

page 1

A318897

Number of tilings of the even-order sphinx with the two dominoes that form the second-order sphinx.

+10
2

1, 8, 5433, 28925040

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,2

COMMENTS

There are 46 sphinx dominoes. The order 2 sphinx is composed of two different dominoes. These two dominoes are used to tile the even-order sphinx.

The orientation of the order 8 sphinx in the link below is essential for the bit-vector bottom-up search to efficiently find solutions. All order 8 solutions are found in a few minutes.

LINKS

Table of n, a(n) for n=1..4.

Craig Knecht, 46 sphinx dominoes.

Craig Knecht, Sphinx domino introduction.

Craig Knecht, Sphinx domino tiling.

Craig Knecht, T12 missing one of the fundamental two dominoes.

CROSSREFS

Cf. A279887, A317541.

KEYWORD

nonn,more

AUTHOR

Craig Knecht, Sep 05 2018

STATUS

approved

A318778

Number of different positions that an elementary sphinx can occupy in a sphinx of order n.

+10
1

1, 28, 128, 300, 544, 860, 1248, 1708, 2240, 2844

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,2

LINKS

Table of n, a(n) for n=1..10.

Craig Knecht, 33 positions that a flacon occupies in a S4 sphinx - animated.

Craig Knecht, Bottom row surface tension.

Craig Knecht, Order Two Sphinx - 28 positions.

Craig Knecht, Order three sphinx - 128 positions.

Craig Knecht, Various shapes positioned in a order 4 sphinx.

FORMULA

Conjectures from Colin Barker, Nov 13 2018: (Start)

G.f.: x*(1 + 25*x + 47*x^2 - x^3) / (1 - x)^3.

a(n) = 44 - 80*n + 36*n^2 for n>1.

a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>4.

(End)