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 A211521 #34 Sep 08 2022 08:46:02
%S A211521 0,0,1,2,4,5,9,11,16,18,25,28,36,39,49,53,64,68,81,86,100,105,121,127,
%T A211521 144,150,169,176,196,203,225,233,256,264,289,298,324,333,361,371,400,
%U A211521 410,441,452,484,495,529,541,576,588,625,638,676,689,729,743
%N A211521 Number of ordered triples (w,x,y) with all terms in {1,...,n} and w + 2x = 4y.
%C A211521 For a guide to related sequences, see A211422.
%C A211521 Also, number of ordered pairs (w,x) with both terms in {1,...,n} and w+2x divisible by 4. - _Pontus von Brömssen_, Jan 19 2020
%H A211521 Colin Barker, <a href="/A211521/b211521.txt">Table of n, a(n) for n = 0..999</a>
%H A211521 <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (1,1,-1,1,-1,-1,1).
%F A211521 a(n) = a(n-1) + a(n-2) - a(n-3) + a(n-4) - a(n-5) - a(n-6) + a(n-7).
%F A211521 a(n) = (2*n^2-n+1+(n-1)*(-1)^n+(-1)^((2*n+1-(-1)^n)/4)-(-1)^((6*n+1-(-1)^n)/4))/8. - _Luce ETIENNE_, Dec 31 2015
%F A211521 G.f.: x^2*(1 + x + x^2 + x^4) / ((1 - x)^3*(1 + x)^2*(1 + x^2)). - _Colin Barker_, Dec 02 2017
%t A211521 t[n_] := t[n] = Flatten[Table[w + 2 x - 4 y, {w, 1, n}, {x, 1, n}, {y, 1, n}]]
%t A211521 c[n_] := Count[t[n], 0]
%t A211521 t = Table[c[n], {n, 0, 70}] (* A211521 *)
%t A211521 FindLinearRecurrence[t]
%t A211521 LinearRecurrence[{1,1,-1,1,-1,-1,1},{0,0,1,2,4,5,9},56] (* _Ray Chandler_, Aug 02 2015 *)
%o A211521 (PARI) concat(vector(2), Vec(x^2*(1 + x + x^2 + x^4) / ((1 - x)^3*(1 + x)^2*(1 + x^2)) + O(x^40))) \\ _Colin Barker_, Dec 02 2017
%o A211521 (Magma) a:=[0]; for n in [1..55] do m:=0; for i, j in [1..n] do if (i+2*j) mod 4 eq 0 then m:=m+1; end if; end for; Append(~a, m); end for; a; // _Marius A. Burtea_, Jan 19 2020
%o A211521 (Magma) R<x>:=PowerSeriesRing(Integers(), 57); [0,0] cat Coefficients(R!( x^3*(1 + x + x^2 + x^4) / ((1 - x)^3*(1 + x)^2*(1 + x^2)))); // _Marius A. Burtea_, Jan 19 2020
%Y A211521 Cf. A211422.
%K A211521 nonn,easy
%O A211521 0,4
%A A211521 _Clark Kimberling_, Apr 14 2012
%E A211521 Offset corrected by _Pontus von Brömssen_, Jan 19 2020