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 A212899 Number of (w,x,y,z) with all terms in {0,...,n} and (least gapsize)>2. 3

%I

%S 0,0,0,2,16,62,186,456,962,1818,3162,5156,7986,11862,17018,23712,

%T 32226,42866,55962,71868,90962,113646,140346,171512,207618,249162,

%U 296666,350676,411762,480518,557562,643536,739106,844962,961818

%N Number of (w,x,y,z) with all terms in {0,...,n} and (least gapsize)>2.

%C The gapsizes are |w-x|, |x-y|, |y-z|. Every term is even. a(n)+A212898(n)=(n+1)^4.

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

%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (5, -10, 10, -5, 1).

%F a(n)=5*a(n-1)+10*a(n-2)-10*a(n-3)+5*a(n-4)-a(n-5) for n>=9.

%F G.f.: (2*x^3 + 6*x^4 + 2*x^5 + 16*x^6 - 4*x^7 + 2*x^9 )/(1 - 5*x + 10*x^2 - 10*x^3 + 5*x^4 - x^5)

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

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

%t {w, 0, n}, {x, 0, n}, {y, 0, n}, {z, 0, n}]; s)]];

%t m = Map[t[#] &, Range[0, 40]] (* A212899 *)

%t m/2 (* integers *)

%Y Cf. A211795.

%K nonn,easy

%O 0,4

%A _Clark Kimberling_, May 31 2012

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Last modified December 2 11:44 EST 2021. Contains 349440 sequences. (Running on oeis4.)