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Number of n-step polygons on f.c.c. lattice.
(Formerly M4512)
2

%I M4512 #34 Apr 05 2024 19:46:30

%S 8,33,168,970,6168,42069,301376,2241420,17173224,134806948,1079802216,

%T 8798329080,72748583832,609220407150,5158999447488

%N Number of n-step polygons on f.c.c. lattice.

%D A. J. Guttmann, Polygons, Polyominoes and Polycubes, Lecture Notes in Physics Volume 775, 2009, Chapter 16.

%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

%H M. F. Sykes et al., <a href="http://dx.doi.org/10.1063/1.1705066">Lattice constant systems and graph theory</a>, J. Math. Phys., 7 (1966), 1557-1572.

%H <a href="/index/Fa#fcc">Index entries for sequences related to f.c.c. lattice</a>

%t A001337 = Cases[Import["https://oeis.org/A001337/b001337.txt", "Table"], {_, _}][[All, 2]];

%t a[n_] := A001337[[n]]/(2n);

%t a /@ Range[3, 17] (* _Jean-François Alcover_, Jan 20 2020 *)

%Y Equals A001337(n) / (2n).

%K nonn,more,nice

%O 3,1

%A _N. J. A. Sloane_

%E More terms from _Ruperto Corso_, Dec 19 2011

%E a(15) and a(16) from _Sean A. Irvine_, Mar 30 2017

%E a(17) from _Bert Dobbelaere_, Jan 14 2019