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A179167
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Place a(n) red and b(n) blue balls in an urn; draw 3 balls without replacement; Probability(3 red balls) = Probability(1 red and 2 blue balls); binomial(a(n),3) = binomial(a(n),1)*binomial(b(n),2).
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1
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3, 4, 11, 37, 134, 496, 1847, 6889, 25706, 95932, 358019, 1336141, 4986542, 18610024, 69453551, 259204177, 967363154, 3610248436, 13473630587, 50284273909, 187663465046, 700369586272, 2613814880039, 9754889933881
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OFFSET
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1,1
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LINKS
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FORMULA
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a(n+2) = 4*a(n+1) - a(n) - 3;
a(n+3) = 5*(a(n+2) - a(n+1)) + a(n); r=sqrt(3);
a(n) = (6 + (1+r)*(2+r)^(n-1) + (1-r)*(2-r)^(n-1))/4;
a(n) = ceiling((6 + (1+r)*(2+r)^(n-1))/4).
a(n) = 5*a(n-1) - 5*a(n-2) + a(n-3) for n > 4.
G.f.: x*(x^3-6*x^2+11*x-3) / ((x-1)*(x^2-4*x+1)). (End)
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EXAMPLE
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For n=4, a(4)=37; b(4)=21; binomial(37,3) = 7770;
binomial(37,1)*binomial(21,2) = 37*210 = 7770.
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MAPLE
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r:=sqrt(3): for n from 1 to 40 do
a(n):=(6+(1+r)*(2+r)^(n-1)+(1-r)*(2-r)^(n-1))/4: end do:
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CROSSREFS
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KEYWORD
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nonn,uned,easy
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AUTHOR
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STATUS
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approved
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