|
%I #13 Jun 23 2021 08:30:07
%S 0,0,0,0,0,0,0,0,0,1,1,1,1,2,3,3,3,4,5,6,6,7,8,9,10,11,12,13,14,16,17,
%T 18,19,21,23,24,25,27,29,31,32,34,36,38,40,42,44,46,48,51,53,55,57,60,
%U 63,65,67,70,73,76,78,81,84,87,90,93,96,99,102,106,109
%N Number of ordered triples (w,x,y) with all terms in {1,...,n} and w=4x+5y.
%C For a guide to related sequences, see A211422.
%H Colin Barker, <a href="/A211535/b211535.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_10">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,0,1,0,-1,0,0,-1,1).
%F a(n) = a(n-1) + a(n-4) - a(n-6) - a(n-9) + a(n-10).
%F G.f.: x^9 / ((1 - x)^3*(1 + x)*(1 + x^2)*(1 + x + x^2 + x^3 + x^4)). - _Colin Barker_, Dec 03 2017
%F a(n)-a(n-1)=A165190(n-9). - _R. J. Mathar_, Jun 23 2021
%t t[n_] := t[n] = Flatten[Table[-w + 4 x + 5 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}] (* A211535 *)
%t FindLinearRecurrence[t]
%t LinearRecurrence[{1,0,0,1,0,-1,0,0,-1,1},{0,0,0,0,0,0,0,0,0,1},71] (* _Ray Chandler_, Aug 02 2015 *)
%o (PARI) concat(vector(9), Vec(x^9 / ((1 - x)^3*(1 + x)*(1 + x^2)*(1 + x + x^2 + x^3 + x^4)) + O(x^100))) \\ _Colin Barker_, Dec 03 2017
%Y Cf. A211422, A205772.
%K nonn,easy
%O 0,14
%A _Clark Kimberling_, Apr 15 2012
|
