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 A211547 #32 Oct 26 2024 22:57:09
%S A211547 0,0,0,1,1,1,4,4,4,9,9,9,16,16,16,25,25,25,36,36,36,49,49,49,64,64,64,
%T A211547 81,81,81,100,100,100,121,121,121,144,144,144,169,169,169,196,196,196,
%U A211547 225,225,225,256,256,256,289,289,289,324,324,324,361,361,361
%N A211547 The squares n^2, n >= 0, each one written three times.
%C A211547 Number of ordered triples (w,x,y) with all terms in {1,...,n} and 2w=3x+3y.
%C A211547 For a guide to related sequences, see A211422.
%H A211547 Colin Barker, <a href="/A211547/b211547.txt">Table of n, a(n) for n = 0..1000</a>
%H A211547 <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,2,-2,0,-1,1).
%F A211547 a(n) = a(n-1) + 2*a(n-3) - 2*a(n-4) - a(n-6) + a(n-7).
%F A211547 G.f.: x^3*(1 + x)*(1 - x + x^2) / ((1 - x)^3*(1 + x + x^2)^2). - _Colin Barker_, Dec 02 2017
%F A211547 a(n) = A075561(n-2) for n > 2. - _Georg Fischer_, Oct 23 2018
%F A211547 E.g.f.: exp(-x/2)*(exp(3*x/2)*(5 + 3*x*(x - 1)) - 5*cos(sqrt(3)*x/2) - sqrt(3)*(3 + 4*x)*sin(sqrt(3)*x/2))/27. - _Stefano Spezia_, Oct 17 2022
%t A211547 t[n_] := t[n] = Flatten[Table[-2 w + 3 x + 3 y, {w, 1, n}, {x, 1, n}, {y, 1, n}]]
%t A211547 c[n_] := Count[t[n], 0]
%t A211547 t = Table[c[n], {n, 0, 60}](*A211547, squares thrice*)
%t A211547 FindLinearRecurrence[t]
%t A211547 LinearRecurrence[{1,0,2,-2,0,-1,1},{0,0,0,1,1,1,4},60] (* _Ray Chandler_, Aug 02 2015 *)
%o A211547 (PARI) concat(vector(3), Vec(x^3*(1 + x)*(1 - x + x^2) / ((1 - x)^3*(1 + x + x^2)^2) + O(x^40))) \\\ _Colin Barker_, Dec 02 2017
%Y A211547 Cf. A075561, A211422, A211435 (triply repeated triangular numbers).
%K A211547 nonn,easy
%O A211547 0,7
%A A211547 _Clark Kimberling_, Apr 15 2012
%E A211547 Definition simplified by _N. J. A. Sloane_, Nov 17 2020. Also the old version said "squares repeated three times", which was at best ambiguous, and strictly speaking was incorrect, since "squares repeated" is 0, 0, 1, 1, 4, 4, 9, 9, ... .