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A212567 Number of (w,x,y,z) with all terms in {1,...,n} and 2w+2x=3y+3z.

%I A212567 #12 Feb 17 2024 14:05:04
%S A212567 0,0,2,5,11,27,42,68,106,149,201,279,354,452,572,701,845,1031,1212,
%T A212567 1428,1676,1937,2219,2559,2892,3272,3694,4133,4599,5139,5670,6260,
%U A212567 6902,7565,8261,9047,9822,10668,11576,12509,13481,14559,15624,16772
%N A212567 Number of (w,x,y,z) with all terms in {1,...,n} and 2w+2x=3y+3z.
%C A212567 For a guide to related sequences, see A211795.
%H A212567 <a href="/index/Rec#order_10">Index entries for linear recurrences with constant coefficients</a>, signature (0,2,2,-1,-4,-1,2,2,0,-1).
%F A212567 a(n) = 2*a(n-2)+2*a(n-3)-a(n-4)-4*a(n-5)-a(n-6)+2*a(n-7)+2*a(n-8)-a(n-10).
%F A212567 G.f.: x^2*(2+5*x+7*x^2+13*x^3+12*x^4+5*x^5+x^6+x^7)/((1+x)^2*(1-x)^4*(1+x+x^2)^2). [_Bruno Berselli_, May 06 2012]
%t A212567 t = Compile[{{n, _Integer}}, Module[{s = 0},
%t A212567 (Do[If[2 w + 2 x == 3 y + 3 z, s = s + 1],
%t A212567 {w, 1, #}, {x, 1, #}, {y, 1, #}, {z, 1, #}] &[n]; s)]];
%t A212567 Map[t[#] &, Range[0, 50]]   (* A212567 *)
%o A212567 (Maxima) makelist(coeff(taylor(x^2*(2+5*x+7*x^2+13*x^3+12*x^4+5*x^5+x^6+x^7)/((1+x)^2*(1-x)^4*(1+x+x^2)^2), x, 0, n), x, n), n, 0, 43); /* _Bruno Berselli_, May 06 2012 */
%Y A212567 Cf. A211795.
%K A212567 nonn,easy
%O A212567 0,3
%A A212567 _Clark Kimberling_, May 22 2012