|
%I #12 Dec 03 2017 13:56:02
%S 0,0,0,2,3,4,9,11,13,21,24,27,38,42,46,60,65,70,87,93,99,119,126,133,
%T 156,164,172,198,207,216,245,255,265,297,308,319,354,366,378,416,429,
%U 442,483,497,511,555,570,585,632,648,664,714,731,748,801,819
%N Number of ordered triples (w,x,y) with all terms in {1,...,n} and w=3x-3y.
%C For a guide to related sequences, see A211422.
%H Colin Barker, <a href="/A211546/b211546.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,2,-2,0,-1,1).
%F a(n) = a(n-1) + 2*a(n-3) - 2*a(n-4) - a(n-6) + a(n-7).
%F G.f.: x^3*(2 + x + x^2 + x^3) / ((1 - x)^3*(1 + x + x^2)^2). - _Colin Barker_, Dec 03 2017
%t t[n_] := t[n] = Flatten[Table[w - 3 x + 3 y, {w, 1, n}, {x, 1, n}, {y, 1, n}]]
%t c[n_] := Count[t[n], 0]
%t t = Table[c[n], {n, 0, 70}] (* A211546 *)
%t FindLinearRecurrence[t]
%t LinearRecurrence[{1,0,2,-2,0,-1,1},{0,0,0,2,3,4,9},56] (* _Ray Chandler_, Aug 02 2015 *)
%o (PARI) concat(vector(3), Vec(x^3*(2 + x + x^2 + x^3) / ((1 - x)^3*(1 + x + x^2)^2) + O(x^40))) \\ _Colin Barker_, Dec 03 2017
%Y Cf. A211422.
%K nonn,easy
%O 0,4
%A _Clark Kimberling_, Apr 15 2012
|
