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 A267489 #27 Sep 08 2022 08:46:15
%S A267489 0,1,4,5,8,9,12,17,24,29,36,41,48,57,68,77,88,97,108,121,136,149,164,
%T A267489 177,192,209,228,245,264,281,300,321,344,365,388,409,432,457,484,509,
%U A267489 536,561,588,617,648,677,708,737,768,801,836,869,904
%N A267489 a(n) = n^2 - 4*floor(n^2/6).
%C A267489 Inspired by A137932 and A042948.
%C A267489 The pattern is generated by adding subdiagonals parallel to principal diagonals at a spacing of at least 1 box in any direction from the previous generation.
%C A267489 Conjectures:
%C A267489 (i) a(n) is the total number of boxes (or 1's) at the n-th iteration.
%C A267489 (ii) The total number of left boxes (or 0's) is 4*A056827.
%H A267489 Colin Barker, <a href="/A267489/b267489.txt">Table of n, a(n) for n = 0..1000</a>
%H A267489 Kival Ngaokrajang, <a href="/A267489/a267489.pdf">Illustration of initial terms</a>
%H A267489 <a href="/index/Rec#order_08">Index entries for linear recurrences with constant coefficients</a>, signature (2,-1,0,0,0,1,-2,1).
%F A267489 a(n) = n^2 - 4*floor(n^2/6) for n >= 0.
%F A267489 From _Colin Barker_, Jan 16 2016: (Start)
%F A267489 a(n) = 2*a(n-1) - a(n-2) + a(n-6) - 2*a(n-7) + a(n-8) for n>7.
%F A267489 G.f.: x*(1+2*x-2*x^2+2*x^3-2*x^4+2*x^5+x^6) / ((1-x)^3*(1+x)*(1-x+x^2)*(1+x+x^2)).
%F A267489 (End)
%p A267489 A267489:=n->n^2-4*floor(n^2/6): seq(A267489(n), n=0..100); # _Wesley Ivan Hurt_, Apr 11 2017
%t A267489 Table[n^2 - 4 Floor[n^2 / 6], {n, 0, 70}] (* _Vincenzo Librandi_, Jan 16 2016 *)
%o A267489 (PARI) for (n = 0, 100, a = n^2-4*floor(n^2/6); print1(a, ", "))
%o A267489 (PARI) concat(0, Vec(x*(1+2*x-2*x^2+2*x^3-2*x^4+2*x^5+x^6)/((1-x)^3*(1+x)*(1-x+x^2)*(1+x+x^2)) + O(x^100))) \\ _Colin Barker_, Jan 16 2016
%o A267489 (PARI) a(n)=n^2 - n^2\6*4 \\ _Charles R Greathouse IV_, Mar 22 2017
%o A267489 (Magma) [0] cat [n^2-4*Floor(n^2/6): n in [1..70]]; // _Vincenzo Librandi_, Jan 16 2016
%Y A267489 Cf. A042948, A056827, A137932.
%K A267489 nonn,easy
%O A267489 0,3
%A A267489 _Kival Ngaokrajang_, Jan 16 2016