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 A124745 #32 Jan 10 2025 04:39:22
%S A124745 1,1,1,0,0,-1,0,-1,1,-1,2,-2,3,-4,5,-7,9,-12,16,-21,28,-37,49,-65,86,
%T A124745 -114,151,-200,265,-351,465,-616,816,-1081,1432,-1897,2513,-3329,4410,
%U A124745 -5842,7739,-10252,13581,-17991,23833,-31572,41824,-55405,73396,-97229,128801
%N A124745 Expansion of (1+x)/(1-x^2+x^3).
%H A124745 Paolo Xausa, <a href="/A124745/b124745.txt">Table of n, a(n) for n = 0..1000</a>
%H A124745 Yuksel Soykan, Vedat Irge, and Erkan Tasdemir, <a href="https://doi.org/10.9734/ajpas/2024/v26i12691">A Comprehensive Study of K-Circulant Matrices Derived from Generalized Padovan Numbers</a>, Asian Journal of Probability and Statistics 26 (12):152-70, (2024). See p. 154.
%H A124745 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (0,1,-1).
%F A124745 a(n) = Sum_{k=0..n} C(floor(k/2),n-k)*(-1)^(n-k) = (-1)^n*A078027(n).
%F A124745 a(n) = a(n-2) - a(n-3) with a(0) = a(1) = a(2) = 1. - _Taras Goy_, Mar 24 2019
%t A124745 LinearRecurrence[{0, 1, -1}, {1, 1, 1}, 100] (* _Paolo Xausa_, Aug 27 2024 *)
%Y A124745 Row sums of A124744.
%Y A124745 The following are basically all variants of the same sequence: A000931, A078027, A096231, A124745, A133034, A134816, A164001, A182097, A228361 and probably A020720. However, each one has its own special features and deserves its own entry.
%K A124745 easy,sign
%O A124745 0,11
%A A124745 _Paul Barry_, Nov 06 2006