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 A211520 #36 Feb 22 2025 18:38:10
%S A211520 0,0,0,1,2,3,5,7,10,12,16,19,24,27,33,37,44,48,56,61,70,75,85,91,102,
%T A211520 108,120,127,140,147,161,169,184,192,208,217,234,243,261,271,290,300,
%U A211520 320,331,352,363,385,397,420,432,456,469,494,507,533,547,574
%N A211520 Number of ordered triples (w,x,y) with all terms in {1,...,n} and w + 4y = 2x.
%C A211520 For a guide to related sequences, see A211422.
%H A211520 Reinhard Zumkeller, <a href="/A211520/b211520.txt">Table of n, a(n) for n = 0..10000</a>
%H A211520 <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (1,1,-1,1,-1,-1,1).
%F A211520 a(n) = a(n-1) + a(n-2) - a(n-3) + a(n-4) - a(n-5) - a(n-6) + a(n-7).
%F A211520 a(n) - a(n-1) = A178804(n-2). - _Reinhard Zumkeller_, Nov 15 2014
%F A211520 a(n) = (6*n^2-10*n+3+(2*n-7)*(-1)^n-4*(-1)^((2*n-3-(-1)^n)/4))/32. - _Luce ETIENNE_, Dec 31 2015
%F A211520 a(n) = Sum_{k=1..floor(n/2)} floor((n-k)/2). - _Wesley Ivan Hurt_, Apr 01 2017
%F A211520 G.f.: x^3 * (1+x+x^3) / ( (1-x)^3*(1+x)^2*(1+x^2) ). - _Joerg Arndt_, Apr 02 2017
%F A211520 a(n)+a(n-1) = A282513(n-2). - _R. J. Mathar_, Jun 23 2021
%F A211520 a(n) = floor((n-1)^2/4) - floor((n-1)/4)*floor((n+1)/4). - _Ridouane Oudra_, Nov 21 2024
%p A211520 seq(floor((n-1)^2/4)-floor((n-1)/4)*floor((n+1)/4), n=0..60); # _Ridouane Oudra_, Nov 21 2024
%t A211520 t[n_] := t[n] = Flatten[Table[w - 2 x + 4 y, {w, 1, n}, {x, 1, n}, {y, 1, n}]]
%t A211520 c[n_] := Count[t[n], 0]
%t A211520 t = Table[c[n], {n, 0, 70}] (* this sequence *)
%t A211520 FindLinearRecurrence[t]
%t A211520 LinearRecurrence[{1,1,-1,1,-1,-1,1},{0,0,0,1,2,3,5},57] (* _Ray Chandler_, Aug 02 2015 *)
%o A211520 (Haskell)
%o A211520 a211520 n = a211520_list !! n
%o A211520 a211520_list = 0 : 0 : 0 : scanl1 (+) a178804_list
%o A211520 -- _Reinhard Zumkeller_, Nov 15 2014
%o A211520 (PARI) { my(x='x+O('x^66)); concat([0,0,0],Vec( x^3*(1+x+x^3) / ( (1-x)^3*(1+x)^2*(1+x^2) ) ) ) } \\ _Joerg Arndt_, Apr 02 2017
%Y A211520 Cf. A178804, A211422, A282513.
%K A211520 nonn,easy
%O A211520 0,5
%A A211520 _Clark Kimberling_, Apr 14 2012