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The number of free polyiamonds with n cells on an order-7 triangular tiling of the hyperbolic plane.
3

%I #32 Feb 15 2021 01:56:42

%S 1,1,1,1,3,4,12,27,78,208,637,1870,5797,17866,56237,177573,566904,

%T 1818527,5874180,19065038

%N The number of free polyiamonds with n cells on an order-7 triangular tiling of the hyperbolic plane.

%C This gives the number of polyforms with n cells in the hyperbolic tiling with Schläfli symbol {3,7}.

%C This sequence is computed from via program by _Christian Sievers_ in the Code Golf Stack Exchange link.

%H Code Golf Stack Exchange, <a href="https://codegolf.stackexchange.com/a/200295/53884">Impress Donald Knuth by counting polyominoes on the hyperbolic plane</a>

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Order-7_triangular_tiling">Order-7 triangular tiling</a>

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Polyiamond">Polyiamond</a>

%o Several working programs are available via the Code Golf link.

%Y Analogs with different Schläfli symbols are A000207 ({3,oo}), A000577 ({3,6}), A005036 ({4,oo}), and A119611 ({4,5}).

%K nonn,more

%O 0,5

%A _Peter Kagey_, Mar 01 2020

%E a(11)-a(19) from _Ed Wynn_, Feb 14 2021