cp's OEIS Frontend

A212898 Number of (w,x,y,z) with all terms in {0,...,n} and (least gapsize)<=2.

%I A212898 #17 Jun 17 2017 02:59:43
%S A212898 1,16,81,254,609,1234,2215,3640,5599,8182,11479,15580,20575,26554,
%T A212898 33607,41824,51295,62110,74359,88132,103519,120610,139495,160264,
%U A212898 183007,207814,234775,263980,295519,329482,365959,405040,446815,491374
%N A212898 Number of (w,x,y,z) with all terms in {0,...,n} and (least gapsize)<=2.
%C A212898 The gapsizes are |w-x|, |x-y|, |y-z|.
%C A212898 a(n)+A212899(n) = (n+1)^4.
%C A212898 For a guide to related sequences, see A211795.
%H A212898 Vincenzo Librandi, <a href="/A212898/b212898.txt">Table of n, a(n) for n = 0..1000</a>
%H A212898 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (4,-6,4,-1).
%F A212898 a(n) = 4*a(n-1)-6*a(n-2)+4*a(n-3)-a(n-4) for n>=9.
%F A212898 G.f.: (1 + 12*x + 23*x^2 + 22*x^3 + 16*x^4 + 14*x^5 - 2*x^6 + 2*x^7 + 2*x^8)/(1 - x)^4.
%F A212898 a(n) = 15*n^3-48*n^2+144*n-161 with n>4, a(0)=1, a(1)=16, a(2)=81, a(3)=254, a(4)=609. [_Bruno Berselli_, Jun 12 2012]
%t A212898 t = Compile[{{n, _Integer}}, Module[{s = 0},
%t A212898 (Do[If[Min[Abs[w - x], Abs[x - y], Abs[y - z]] <= 2, s = s + 1],
%t A212898 {w, 0, n}, {x, 0, n}, {y, 0, n}, {z, 0, n}]; s)]];
%t A212898 m = Map[t[#] &, Range[0, 40]]   (* A212898 *)
%t A212898 CoefficientList[Series[(1+12*x+23*x^2+22*x^3+16*x^4+14*x^5-2*x^6+ 2*x^7+ 2*x^8)/(1-x)^4,{x,0,40}],x] (* _Vincenzo Librandi_, Jul 04 2012 *)
%Y A212898 Cf. A211795.
%K A212898 nonn,easy
%O A212898 0,2
%A A212898 _Clark Kimberling_, May 31 2012