A069788 - OEIS

%I #14 Jan 11 2025 03:34:39

%S 2,54,4320,2500000,5252187500,68336412238080,3507134014317846528,

%T 1039468958911770833166336,1271288794044247678785011427072,

%U 8629570422218326431392139107794299444,248662702551142788293946930136251315440514048,38763625610496798571986566181715696354290667009540096

%N Number of tilings by lozenges of hexagon with sides n, n+1, n, n+1, n, n+1 and central triangle removed.

%D J. Propp, Enumeration of matchings: problems and progress, pp. 255-291 in L. J. Billera et al., eds, New Perspectives in Algebraic Combinatorics, Cambridge, 1999 (see Problem 1).

%H Harald A. Helfgott and Ira M. Gessel, <a href="https://doi.org/10.37236/1448">Tilings of Diamonds and Hexagons with Defects</a>, Electron. J. Combin., 6 (1999) (see Theorem 20).

%H Sean A. Irvine, <a href="https://github.com/archmageirvine/joeis/blob/master/src/irvine/oeis/a069/A069788.java">Java program</a> (github)

%H J. Propp, <a href="http://faculty.uml.edu/jpropp/update.pdf">Updated article</a>

%H J. Propp, Enumeration of matchings: problems and progress, in L. J. Billera et al. (eds.), <a href="http://www.msri.org/publications/books/Book38/contents.html">New Perspectives in Algebraic Combinatorics</a>

%K nonn,easy

%O 1,1

%A _N. J. A. Sloane_, May 28 2002

%E Propp gives 12 terms.

%E More terms from Antonio G. Astudillo (afg_astudillo(AT)lycos.com), Mar 30 2003