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%I #12 Feb 20 2024 03:37:10
%S 1,1,2,4,7,9,12,16,21,25,30,36,43,49,56,64,73,81,90,100,111,121,132,
%T 144,157,169,182,196,211,225,240,256,273,289,306,324,343,361,380,400,
%U 421,441,462,484,507,529,552,576,601,625,650,676,703,729,756,784
%N Number of (w,x,y) with all terms in {0,...,n} and 4*w = x+y.
%C For a guide to related sequences, see A212959.
%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (2,-1,0,1,-2,1).
%F a(n) = 2*a(n-1)-a(n-2)+a(n-4)-2*a(n-5)+a(n-6).
%F G.f.: f(x)/g(x), where f(x) = 1 - x + x^2 + x^3
%F and g(x) = (1 + x + x^2 + x^3)(1-x)^3.
%t t = Compile[{{n, _Integer}}, Module[{s = 0}, (Do[If[4 w == x + y, s = s + 1], {w, 0, n}, {x, 0, n}, {y, 0, n}]; s)]];
%t m = Map[t[#] &, Range[0, 70]] (* A212988 *)
%Y Cf. A212959.
%K nonn,easy
%O 0,3
%A _Clark Kimberling_, Jun 04 2012
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