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 A345448 #29 Nov 11 2024 09:01:15
%S A345448 1,1,2,7,15,32,79,185,422,987,2307,5352,12451,29005,67478,156991,
%T A345448 365391,850304,1978615,4604465,10715078,24934611,58024779,135028632,
%U A345448 314222011,731218981,1701605078,3959769367,9214694391,21443322032,49900304047,116121942377
%N A345448 Number of tilings of a 2 X n rectangle with dominoes and long L-shaped 4-minoes.
%H A345448 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (1,1,4,2).
%F A345448 a(n) = a(n-1) + a(n-2) + 4*a(n-3) + 2*a(n-4).
%F A345448 Sum_{j=0..n} a(n) = (1/7)(a(n+4) - a(n+2) - 5*a(n+1) - 1).
%F A345448 G.f.: 1/(1 - x - x^2 - 4*x^3 - 2*x^4). - _Stefano Spezia_, Jun 19 2021
%F A345448 a(n) = F(n+1) + 2*Sum_{j=3..n} a(n-j)*F(j) for F(i) = A000045(i) the i-th Fibonacci number. - _Greg Dresden_, Nov 10 2024
%e A345448 For n = 3 the a(3)=7 tilings are:
%e A345448 ._____. ._____. ._____. ._____.
%e A345448 | |___| |___| | | ___| |___ |
%e A345448 |_____| |_____| |_|___| |___|_|
%e A345448 ._____. ._____. ._____.
%e A345448 |___| | | |___| | | | |
%e A345448 |___|_| |_|___| |_|_|_|
%t A345448 LinearRecurrence[{1, 1, 4, 2}, {1, 1, 2, 7}, 40]
%Y A345448 Cf. A052980.
%K A345448 nonn,easy
%O A345448 0,3
%A A345448 _Greg Dresden_ and _Yiwen Zhang_, Jun 19 2021