cp's OEIS Frontend

A212757 Number of (w,x,y,z) with all terms in {0,...,n} and 2w=max{w,x,y,z}-min{w,x,y,z}.

%I A212757 #9 Jun 13 2015 00:54:14
%S A212757 1,1,13,32,56,80,177,213,297,472,580,688,1037,1169,1385,1872,2124,
%T A212757 2376,3133,3421,3829,4784,5240,5696,7017,7521,8181,9760,10480,11200,
%U A212757 13241,14021,14993,17352,18396,19440,22357,23473,24817,28112,29540
%N A212757 Number of (w,x,y,z) with all terms in {0,...,n} and 2w=max{w,x,y,z}-min{w,x,y,z}.
%C A212757 For a guide to related sequences, see A211795.
%H A212757 <a href="/index/Rec#order_12">Index entries for linear recurrences with constant coefficients</a>, signature (-1,1,4,3,-3,-6,-3,3,4,1,-1,-1)
%F A212757 a(n)=-a(n-1)+a(n-2)+4*a(n-3)+3*a(n-4)-3*a(n-5)-6*a(n-6)-3*a(n-7)+3*a(n-8)+4*a(n-9)+a(n-10)-a(n-11)-a(n-12).
%F A212757 G.f.:  ( 1+2*x+13*x^2+40*x^3+68*x^4+52*x^5+43*x^6+38*x^7+19*x^8 ) / ( (1+x)^2*(1+x+x^2)^3*(x-1)^4 ).
%t A212757 t = Compile[{{n, _Integer}}, Module[{s = 0},
%t A212757 (Do[If[2 w == Max[w, x, y, z] - Min[w, x, y, z], s = s + 1], {w, 0, n}, {x, 0, n}, {y, 0, n}, {z, 0, n}]; s)]];
%t A212757 Map[t[#] &, Range[0, 45]]   (* A212757 *)
%t A212757 LinearRecurrence[{-1, 1, 4, 3, -3, -6, -3, 3, 4, 1, -1, -1}, {1, 1, 13, 32, 56, 80, 177, 213, 297, 472, 580, 688}, 45]
%Y A212757 Cf. A211795.
%K A212757 nonn,easy
%O A212757 0,3
%A A212757 _Clark Kimberling_, May 28 2012