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A016273
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Expansion of g.f. 1/((1-2x)(1-3x)(1-5x)).
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2
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1, 10, 69, 410, 2261, 11970, 61909, 315850, 1598421, 8050130, 40425749, 202656090, 1014866581, 5079099490, 25409813589, 127092049130, 635589254741, 3178333432050, 15892828897429, 79467630222970, 397348609370901, 1986774423719810, 9933966253389269
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OFFSET
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0,2
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LINKS
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FORMULA
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a(n) = Sum_{0<=i,j,k,<=n, i+j+k=n} 2^i*3^j*5^k.
a(n) = (2^(n+3) + 5^(n+2) - 3^(n+3))/6. (End)
a(n) = ((5^n - 2^n)/3 - (3^n - 2^n))/2 , n >= 2. - Zerinvary Lajos, Jun 05 2009
a(n) = 10*a(n-1) - 31*a(n-2) + 30*a(n-3), n >= 3.
a(n) = 8*a(n-1) - 15*a(n-2) + 2^n, a(0)=1, a(1)=10. (End)
E.g.f.: exp(2*x)*(8 - 27*exp(x) + 25*exp(3*x))/6. - Stefano Spezia, Sep 27 2023
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MATHEMATICA
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CoefficientList[ Series[ 1/((1 - 2x)(1 - 3x)(1 - 5x)), {x, 0, 20} ], x ]
LinearRecurrence[{10, -31, 30}, {1, 10, 69}, 20] (* Harvey P. Dale, Oct 05 2014 *)
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PROG
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(Sage) [((5^n - 2^n)/3-(3^n - 2^n))/2 for n in range(2, 22)] # Zerinvary Lajos, Jun 05 2009
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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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