A212689 - OEIS

%I #9 Aug 01 2015 10:26:56

%S 0,0,0,6,20,58,124,244,424,700,1080,1610,2300,3206,4340,5768,7504,

%T 9624,12144,15150,18660,22770,27500,32956,39160,46228,54184,63154,

%U 73164,84350,96740,110480,125600,142256,160480,180438,202164,225834

%N Number of (w,x,y,z) with all terms in {1,...,n} and 2|w-x|>n+|y-z|.

%C a(n)+A212690(n)=n^4.

%C For a guide to related sequences, see A211795.

%H <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (3, -1, -5, 5, 1, -3, 1).

%F a(n)=3*a(n-1)-a(n-2)-5*a(n-3)+5*a(n-4)+a(n-5)-3*a(n-6)+a(n-7).

%F G.f.: (6*x^3 + 2*x^4 + 4*x^5)/(1 - 3*x + x^2 + 5*x^3 - 5*x^4 - x^5 + 3*x^6 - x^7).

%t t = Compile[{{n, _Integer}}, Module[{s = 0},

%t (Do[If[2 Abs[w - x] > n + Abs[y - z], s = s + 1],

%t {w, 1, #}, {x, 1, #}, {y, 1, #}, {z, 1, #}] &[n]; s)]];

%t Map[t[#] &, Range[0, 40]]   (* A212689 *)

%t %/2 (* integers *)

%t LinearRecurrence[{3, -1, -5, 5, 1, -3, 1}, {0, 0, 0, 6, 20, 58, 124}, 40]

%Y Cf. A211795, A212690.

%K nonn,easy

%O 0,4

%A _Clark Kimberling_, May 25 2012