|
%I #14 Feb 20 2024 11:18:38
%S 1,4,11,19,31,44,62,79,103,125,154,181,216,247,288,324,370,411,463,
%T 508,566,616,679,734,803,862,937,1001,1081,1150,1236,1309,1401,1479,
%U 1576,1659,1762,1849,1958,2050,2164,2261,2381,2482,2608,2714,2845
%N Number of (w,x,y) with all terms in {0,...,n} and max(|w-x|,|x-y|) = w.
%C For a guide to related sequences, see A212959.
%H <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (0,2,1,-1,-2,0,1).
%F a(n) = 2*a(n-2) +a(n-3) -a(n-4) -2*a(n-5) +a(n-7).
%F G.f.: (1 +4*x +9*x^2 +10*x^3 +6*x^4 +x^5) / ((1-x)^3*(1+x)^2*(1+x+x^2)).
%t t = Compile[{{n, _Integer}}, Module[{s = 0}, (Do[If[w == Max[Abs[w - x], Abs[x - y]], s = s + 1], {w, 0, n}, {x, 0, n}, {y, 0, n}]; s)]];
%t Map[t[#] &, Range[0, 60]] (* A213395 *)
%o (PARI) a(n)=([0,1,0,0,0,0,0; 0,0,1,0,0,0,0; 0,0,0,1,0,0,0; 0,0,0,0,1,0,0; 0,0,0,0,0,1,0; 0,0,0,0,0,0,1; 1,0,-2,-1,1,2,0]^n*[1;4;11;19;31;44;62])[1,1] \\ _Charles R Greathouse IV_, Nov 27 2016
%Y Cf. A212959.
%K nonn,easy
%O 0,2
%A _Clark Kimberling_, Jun 12 2012
|
