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A100542
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Two-color Rado numbers R(0,n).
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1
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5, 1, 9, 10, 15, 21, 28, 36, 45, 55, 66, 78, 91, 105, 120, 136, 153, 171, 190, 210, 231, 253, 276, 300, 325, 351, 378, 406, 435, 465, 496, 528, 561, 595, 630, 666, 703, 741, 780, 820, 861, 903, 946, 990, 1035, 1081, 1128, 1176, 1225, 1275, 1326, 1378, 1431, 1485, 1540, 1596
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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1,1
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REFERENCES
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S. Burr, S. Loo and D. Schaal, On Rado numbers, I, preprint.
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LINKS
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FORMULA
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After the third term these are simply triangular numbers.
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
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MATHEMATICA
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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 *)
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PROG
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(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
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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