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A212254 Number of (w,x,y,z) with all terms in {1,...,n} and w=x+2y+3z-n.

%I A212254 #19 Jan 05 2025 12:31:33
%S A212254 0,0,0,1,4,11,21,37,59,88,125,172,228,296,376,469,576,699,837,993,
%T A212254 1167,1360,1573,1808,2064,2344,2648,2977,3332,3715,4125,4565,5035,
%U A212254 5536,6069,6636,7236,7872,8544,9253,10000,10787,11613,12481,13391
%N A212254 Number of (w,x,y,z) with all terms in {1,...,n} and w=x+2y+3z-n.
%C A212254 For a guide to related sequences, see A211795.
%H A212254 <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (2,0,-1,-1,0,2,-1).
%F A212254 a(n) = 2*a(n-1)-a(n-3)-a(n-4)+2*a(n-6)-a(n-7).
%F A212254 G.f.: x^3*(3*x^2+2*x+1)/((x-1)^4*(x+1)*(x^2+x+1)). - _Colin Barker_, Oct 07 2012
%t A212254 t = Compile[{{n, _Integer}}, Module[{s = 0},
%t A212254 (Do[If[w == x + 2 y + 3 z - n, s = s + 1],
%t A212254 {w, 1, #}, {x, 1, #}, {y, 1, #}, {z, 1, #}] &[n]; s)]];
%t A212254 Map[t[#] &, Range[0, 40]]  (*  A212254  *)
%t A212254 (* _Peter J. C. Moses_, Apr 13 2012 *)
%Y A212254 Cf. A211795.
%K A212254 nonn,easy
%O A212254 0,5
%A A212254 _Clark Kimberling_, May 15 2012