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 A211533 #15 Apr 09 2025 16:16:49
%S A211533 0,0,1,1,3,4,5,8,10,13,16,19,23,27,32,36,41,47,52,59,65,71,79,86,94,
%T A211533 102,110,119,128,138,147,157,168,178,190,201,212,225,237,250,263,276,
%U A211533 290,304,319,333,348,364,379,396,412,428,446,463,481,499,517,536
%N A211533 Number of ordered triples (w,x,y) with all terms in {1,...,n} and w=3x-5y.
%C A211533 For a guide to related sequences, see A211422.
%H A211533 Colin Barker, <a href="/A211533/b211533.txt">Table of n, a(n) for n = 0..1000</a>
%H A211533 <a href="/index/Rec#order_09">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,1,-1,1,-1,0,-1,1).
%F A211533 a(n) = a(n-1) + a(n-3) - a(n-4) + a(n-5) - a(n-6) - a(n-8) + a(n-9).
%F A211533 G.f.: x^2*(1 + 2*x^2 + x^4 + x^6) / ((1 - x)^3*(1 + x + x^2)*(1 + x + x^2 + x^3 + x^4)). - _Colin Barker_, Dec 02 2017
%F A211533 a(n) ~ n^2/6. - _Stefano Spezia_, Apr 09 2025
%t A211533 t[n_] := t[n] = Flatten[Table[w - 3 x + 5 y, {w, 1, n}, {x, 1, n}, {y, 1, n}]]
%t A211533 c[n_] := Count[t[n], 0]
%t A211533 t = Table[c[n], {n, 0, 70}] (* A211533 *)
%t A211533 FindLinearRecurrence[t]
%t A211533 LinearRecurrence[{1,0,1,-1,1,-1,0,-1,1},{0,0,1,1,3,4,5,8,10},58] (* _Ray Chandler_, Aug 02 2015 *)
%o A211533 (PARI) concat(vector(2), Vec(x^2*(1 + 2*x^2 + x^4 + x^6) / ((1 - x)^3*(1 + x + x^2)*(1 + x + x^2 + x^3 + x^4)) + O(x^40))) \\ _Colin Barker_, Dec 02 2017
%Y A211533 Cf. A211422.
%K A211533 nonn,easy
%O A211533 0,5
%A A211533 _Clark Kimberling_, Apr 15 2012