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 A356889 #22 Jan 07 2024 13:34:06
%S A356889 3,21,125,693,3669,18773,93525,456021,2184533,10310997,48059733,
%T A356889 221599061,1012225365,4585772373,20624790869,92162839893,409453548885,
%U A356889 1809612887381,7960006055253,34863681197397,152099108509013,661172992169301,2864594294232405,12373170851239253
%N A356889 a(n) = (n^2 + 3*n + 10/3)*4^(n-3) - 1/3.
%C A356889 a(n) is the number of fixed polyforms of minimal area (2*n)-1 that contain at least one triangle that touches each side of a triangle formed on a Kagome (trihexagonal) lattice. n is the number of triangles that touch each side of the larger triangle.
%H A356889 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (13,-60,112,-64).
%F A356889 G.f.: x^2*(3 - 18*x + 32*x^2 - 8*x^3)/((1 - x)*(1 - 4*x)^3). - adapted to the offset by _Stefano Spezia_, Sep 03 2022
%F A356889 From _Stefano Spezia_, Sep 03 2022: (Start)
%F A356889 a(n) = (4^n*(10 + 3*n*(3 + n)) - 64)/192.
%F A356889 a(n) = 13*a(n-1) - 60*a(n-2) + 112*a(n-3) - 64*a(n-4) for n > 5. (End)
%e A356889 a(3) = 21. Up to rotations and reflections, there are 5 possibilities:
%e A356889 .
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%t A356889 Table[(n^2 + 3*n + 10/3)*4^(n-3) - 1/3, {n,2,25}] (* _James C. McMahon_, Jan 03 2024 *)
%Y A356889 Cf. A334551.
%K A356889 nonn,easy
%O A356889 2,1
%A A356889 _Jack Hanke_, Sep 02 2022