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%I #16 Mar 28 2023 08:00:15
%S 5,1,9,10,15,21,28,36,45,55,66,78,91,105,120,136,153,171,190,210,231,
%T 253,276,300,325,351,378,406,435,465,496,528,561,595,630,666,703,741,
%U 780,820,861,903,946,990,1035,1081,1128,1176,1225,1275,1326,1378,1431,1485,1540,1596
%N Two-color Rado numbers R(0,n).
%D S. Burr, S. Loo and D. Schaal, On Rado numbers, I, preprint.
%H G. C. Greubel, <a href="/A100542/b100542.txt">Table of n, a(n) for n = 1..5000</a>
%H S. Jones and D. Schaal, <a href="http://dx.doi.org/10.1016/j.disc.2004.06.022">Two-color Rado numbers for x + y + z = kz</a>, Discr. Math., 289 (2004), 63-69.
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F After the third term these are simply triangular numbers.
%F From _Colin Barker_, Jul 30 2013: (Start)
%F a(n) = n*(n+1)/2 for n > 3.
%F a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n > 6.
%F G.f.: x*(5-14*x+21*x^2-19*x^3+11*x^4-3*x^5)/(1-x)^3. (End)
%F E.g.f.: (1/2)*x*(8 - 2*x + x^2 + (2+x)*exp(x) ). - _G. C. Greubel_, Mar 27 2023
%t LinearRecurrence[{3,-3,1},{5,1,9,10,15,21},70] (* _Harvey P. Dale_, Sep 12 2017 *)
%t Join[{5,1,9}, Binomial[Range[5,70], 2]] (* _G. C. Greubel_, Mar 27 2023 *)
%o (Magma) [5,1,9] cat [Binomial(n+1,2): n in [4..70]]; // _G. C. Greubel_, Mar 27 2023
%o (SageMath) [5,1,9]+[binomial(n+1,2) for n in range(4,71)] # _G. C. Greubel_, Mar 27 2023
%Y Cf. A000217.
%K nonn,easy
%O 1,1
%A _N. J. A. Sloane_, Dec 31 2004
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