OFFSET
1,1
REFERENCES
S. Burr, S. Loo and D. Schaal, On Rado numbers, I, preprint.
LINKS
G. C. Greubel, Table of n, a(n) for n = 1..5000
S. Jones and D. Schaal, Two-color Rado numbers for x + y + z = kz, Discr. Math., 289 (2004), 63-69.
Index entries for linear recurrences with constant coefficients, signature (3,-3,1).
FORMULA
After the third term these are simply triangular numbers.
From Colin Barker, Jul 30 2013: (Start)
a(n) = n*(n+1)/2 for n > 3.
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n > 6.
G.f.: x*(5-14*x+21*x^2-19*x^3+11*x^4-3*x^5)/(1-x)^3. (End)
E.g.f.: (1/2)*x*(8 - 2*x + x^2 + (2+x)*exp(x) ). - G. C. Greubel, Mar 27 2023
MATHEMATICA
LinearRecurrence[{3, -3, 1}, {5, 1, 9, 10, 15, 21}, 70] (* Harvey P. Dale, Sep 12 2017 *)
Join[{5, 1, 9}, Binomial[Range[5, 70], 2]] (* G. C. Greubel, Mar 27 2023 *)
PROG
(Magma) [5, 1, 9] cat [Binomial(n+1, 2): n in [4..70]]; // G. C. Greubel, Mar 27 2023
(SageMath) [5, 1, 9]+[binomial(n+1, 2) for n in range(4, 71)] # G. C. Greubel, Mar 27 2023
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
N. J. A. Sloane, Dec 31 2004
STATUS
approved