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 A100312 #19 Feb 01 2023 16:41:55
%S A100312 1,8,32,104,304,832,2176,5504,13568,32768,77824,182272,421888,966656,
%T A100312 2195456,4947968,11075584,24641536,54525952,120061952,263192576,
%U A100312 574619648,1249902592,2709520384,5855248384,12616466432,27111981056,58116276224,124285616128
%N A100312 Number of 3 X n binary matrices avoiding simultaneously the right angled numbered polyomino patterns (ranpp) (10;0) and (01;1).
%C A100312 An occurrence of a ranpp (xy;z) in a matrix A=(a(i,j)) is a triple (a(i1,j1), a(i1,j2), a(i2,j1)) where i1 < i2, j1 < j2 and these elements are in the same relative order as those in the triple (x,y,z). In general, the number of m X n 0-1 matrices in question is given by the g.f. 2*x*y/(1-2*(x+y-x*y)).
%H A100312 G. C. Greubel, <a href="/A100312/b100312.txt">Table of n, a(n) for n = 0..1000</a>
%H A100312 S. Kitaev, <a href="http://www.emis.de/journals/INTEGERS/papers/e21/e21.Abstract.html">On multi-avoidance of right angled numbered polyomino patterns</a>, Integers: Electronic Journal of Combinatorial Number Theory 4 (2004), A21, 20pp.
%H A100312 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (6,-12,8).
%F A100312 G.f.: 1 + 8*x*(1-x)^2/(1-2*x)^3.
%F A100312 a(n) = 2^(n-1) * (n^2 + 5*n + 2).
%F A100312 a(n) = 8 * A049611(n) for n>0.
%F A100312 E.g.f.: (1 + 6*x + 2*x^2)*exp(2*x). - _G. C. Greubel_, Feb 01 2023
%t A100312 Table[2^(n-1)*(n^2+5*n+2), {n,0,50}] (* _G. C. Greubel_, Feb 01 2023 *)
%o A100312 (PARI) vector(50, n, (n^2 + 5*n + 2) * 2^(n-1)) \\ _Michel Marcus_, Dec 01 2014
%o A100312 (Magma) [2^(n-1)*(n^2+5*n+2): n in [0..50]]; // _G. C. Greubel_, Feb 01 2023
%o A100312 (SageMath) [2^(n-1)*(n^2+5*n+2) for n in range(51)] # _G. C. Greubel_, Feb 01 2023
%Y A100312 Cf. A049611, this sequence (m=3), A100313 (m=4).
%K A100312 nonn,easy
%O A100312 0,2
%A A100312 _Sergey Kitaev_, Nov 13 2004
%E A100312 a(0)=1 prepended by _Alois P. Heinz_, Dec 21 2018