A211522 - OEIS

%I #14 Dec 03 2017 02:15:46

%S 0,0,0,1,2,3,4,6,8,11,13,16,19,23,27,31,35,40,45,51,56,62,68,75,82,89,

%T 96,104,112,121,129,138,147,157,167,177,187,198,209,221,232,244,256,

%U 269,282,295,308,322,336,351,365,380,395,411,427,443,459,476

%N Number of ordered triples (w,x,y) with all terms in {1,...,n} and w + 5y = 2x.

%C For a guide to related sequences, see A211422.

%H Colin Barker, <a href="/A211522/b211522.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_08">Index entries for linear recurrences with constant coefficients</a>, signature (1,1,-1,0,1,-1,-1,1).

%F a(n) = a(n-1) + a(n-2) - a(n-3) + a(n-5) - a(n-6) - a(n-7) + a(n-8).

%F G.f.: x^3*(1 + x + x^4) / ((1 - x)^3*(1 + x)*(1 + x + x^2 + x^3 + x^4)). - _Colin Barker_, Dec 02 2017

%t t[n_] := t[n] = Flatten[Table[w - 2 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}]  (* A211522 *)

%t FindLinearRecurrence[t]

%t LinearRecurrence[{1,1,-1,0,1,-1,-1,1},{0,0,0,1,2,3,4,6},58] (* _Ray Chandler_, Aug 02 2015 *)

%o (PARI) concat(vector(3), Vec(x^3*(1 + x + x^4) / ((1 - x)^3*(1 + x)*(1 + x + x^2 + x^3 + x^4)) + O(x^40))) \\ _Colin Barker_, Dec 02 2017

%Y Cf. A211422.

%K nonn,easy

%O 0,5

%A _Clark Kimberling_, Apr 14 2012