This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A356888 #26 Oct 07 2024 03:23:24
%S A356888 1,3,12,44,144,432,1216,3264,8448,21248,52224,125952,299008,700416,
%T A356888 1622016,3719168,8454144,19070976,42729472,95158272,210763776,
%U A356888 464519168,1019215872,2227175424,4848615424,10519314432,22749904896,49056579584,105495134208,226291089408
%N A356888 a(n) = ((n-1)^2 + 2)*2^(n-2).
%C A356888 a(n) is the number of fixed polyiamonds of minimal area 2*n-1 that touch each side of a triangle formed in the triangular lattice. n designates the number of triangles that touch each side of the larger triangle.
%H A356888 Paolo Xausa, <a href="/A356888/b356888.txt">Table of n, a(n) for n = 1..1000</a>
%H A356888 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (6,-12,8).
%F A356888 G.f.: -x*(6*x^2-3*x+1)/(2*x-1)^3.
%F A356888 E.g.f.: (exp(2*x)*(3 - 2*x + 4*x^2) - 3)/4. - _Stefano Spezia_, Sep 02 2022
%e A356888 a(3) = 12. Up to rotations and reflections there are 3 possibilities.
%e A356888 * * *
%e A356888 / \ / \ / \
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%e A356888 *-----* *-----* *-----*
%e A356888 / \ / \ / \ /#\ /#\ /#\
%e A356888 / \ / \ / \ /###\ /###\ /###\
%e A356888 *-----*-----* *-----*-----* *-----*-----*
%e A356888 /#\###/#\###/#\ /#\###/#\###/ \ / \###/#\###/ \
%e A356888 /###\#/###\#/###\ /###\#/###\#/ \ / \#/###\#/ \
%e A356888 *-----*-----*-----* *-----*-----*-----* *-----*-----*-----*
%t A356888 A356888[n_] := ((n-1)^2 + 2)*2^(n-2); Array[A356888, 30] (* or *)
%t A356888 LinearRecurrence[{6, -12, 8}, {1, 3, 12}, 30] (* _Paolo Xausa_, Oct 07 2024 *)
%Y A356888 Cf. A334551.
%K A356888 nonn,easy
%O A356888 1,2
%A A356888 _Jack Hanke_, Sep 02 2022