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 A131322 #54 Jan 28 2025 15:58:43
%S A131322 1,1,3,5,12,23,51,103,221,456,965,2009,4227,8833,18540,38803,81363,
%T A131322 170399,357145,748176,1567849,3284833,6883059,14421533,30218028,
%U A131322 63314735,132664227,277968871,582428789,1220356440,2557009709
%N A131322 Row sums of triangle A131321.
%C A131322 Equals INVERT transform of (1, 2, 0, 1, 0, 1, 0, 1, ...). - _Gary W. Adamson_, Apr 28 2009
%C A131322 The sequence is also the INVERT transform of the aerated odd-indexed Fibonacci numbers (i.e., of (1, 0, 2, 0, 5, 0, ...)). Sequence A124400 is the INVERT transform of the aerated even-indexed Fibonacci numbers. - _Gary W. Adamson_, Feb 07 2014
%C A131322 a(n) is the number of tilings of a 4 X 2n rectangle into L tetrominoes (no reflections, only rotations). - _Nicolas Bělohoubek_, Jan 21 2025
%H A131322 Paolo Xausa, <a href="/A131322/b131322.txt">Table of n, a(n) for n = 0..1000</a>
%H A131322 Nicolas Bělohoubek and Antonín Slavík, <a href="https://www2.karlin.mff.cuni.cz/~slavik/papers/L-tetromino-tilings.pdf">L-Tetromino Tilings and Two-Color Integer Compositions</a>, Univ. Karlova (Czechia, 2025). See p. 3.
%H A131322 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (1,3,-1,-1).
%F A131322 G.f.: (1-x^2)/(1 - x - 3x^2 + x^3 + x^4). - _Philippe Deléham_, Jan 21 2012
%F A131322 a(n) = a(n-1) + 3*a(n-2) - a(n-3) - a(n-4), a(0)=1, a(1)=1, a(2)=3, a(3)=5. - _Philippe Deléham_, Jan 21 2012
%F A131322 a(n) = Sum_{m=0..ceiling(n/2)} binomial(n-m,n-2*m)*Fibonacci(n-2*m+1). - _Vladimir Kruchinin_, Jan 26 2013
%F A131322 From _Nicolas Bělohoubek_, Jan 21 2025: (Start)
%F A131322 a(n) = Sum_{m=1..4} (alpha_m * x_m^n). For x_m and alpha_m values see "L-tetromino tilings" article in links.
%F A131322 a(2*n) = A166482(n). (End)
%e A131322 a(4) = 12 = 5 + 0 + 6 + 0 + 1.
%t A131322 LinearRecurrence[{1, 3, -1, -1}, {1, 1, 3, 5}, 50] (* _Paolo Xausa_, Jan 28 2025 *)
%Y A131322 Cf. A166482, A131321, A000045.
%Y A131322 Cf. A124400.
%K A131322 nonn
%O A131322 0,3
%A A131322 _Gary W. Adamson_, Jun 28 2007
%E A131322 a(10)-a(30) from _Philippe Deléham_, Jan 21 2012