cp's OEIS Frontend

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.

A211544 Number of ordered triples (w,x,y) with all terms in {1,...,n} and 2w=3x-5y.

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%I A211544 #12 Dec 03 2017 13:08:12
%S A211544 0,0,0,1,2,3,4,5,8,10,12,15,17,21,25,28,32,36,41,46,51,56,61,68,74,80,
%T A211544 87,93,101,109,116,124,132,141,150,159,168,177,188,198,208,219,229,
%U A211544 241,253,264,276,288,301,314,327,340,353,368,382,396,411,425,441
%N A211544 Number of ordered triples (w,x,y) with all terms in {1,...,n} and 2w=3x-5y.
%C A211544 For a guide to related sequences, see A211422.
%H A211544 Colin Barker, <a href="/A211544/b211544.txt">Table of n, a(n) for n = 0..1000</a>
%H A211544 <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 A211544 a(n) = a(n-1) + a(n-3) - a(n-4) + a(n-5) - a(n-6) - a(n-8) + a(n-9).
%F A211544 G.f.: x^3*(1 + x)*(1 + x^2 - x^3 + x^4) / ((1 - x)^3*(1 + x + x^2)*(1 + x + x^2 + x^3 + x^4)) - _Colin Barker_, Dec 03 2017
%t A211544 t[n_] := t[n] = Flatten[Table[2 w - 3 x + 5 y, {w, 1, n}, {x, 1, n}, {y, 1, n}]]
%t A211544 c[n_] := Count[t[n], 0]
%t A211544 t = Table[c[n], {n, 0, 70}]   (* A211544 *)
%t A211544 FindLinearRecurrence[t]
%t A211544 LinearRecurrence[{1,0,1,-1,1,-1,0,-1,1},{0,0,0,0,1,1,1,2,3},63] (* _Ray Chandler_, Aug 02 2015 *)
%o A211544 (PARI) concat(vector(3), Vec(x^3*(1 + x)*(1 + x^2 - x^3 + x^4) / ((1 - x)^3*(1 + x + x^2)*(1 + x + x^2 + x^3 + x^4)) + O(x^40))) \\ _Colin Barker_, Dec 03 2017
%Y A211544 Cf. A211422.
%K A211544 nonn,easy
%O A211544 0,5
%A A211544 _Clark Kimberling_, Apr 15 2012