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 A016273 Expansion of 1/((1-2x)(1-3x)(1-5x)). 2
 1, 10, 69, 410, 2261, 11970, 61909, 315850, 1598421, 8050130, 40425749, 202656090, 1014866581, 5079099490, 25409813589, 127092049130, 635589254741, 3178333432050, 15892828897429, 79467630222970, 397348609370901, 1986774423719810, 9933966253389269 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 LINKS Index entries for linear recurrences with constant coefficients, signature (10, -31, 30). FORMULA a(n) = Sum_{0<=i,j,k,<=n, i+j+k=n} 2^i*3^j*5^k. - Hieronymus Fischer, Jun 25 2007 a(n) = (2^(n+3) + 5^(n+2) - 3^(n+3))/6. - Hieronymus Fischer, Jun 25 2007 a(n) = ((5^n - 2^n)/3 - (3^n - 2^n))/2 , n >= 2. - Zerinvary Lajos, Jun 05 2009 From Vincenzo Librandi, Mar 15 2011: (Start) 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) MATHEMATICA 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 *) PROG (Sage) [((5^n - 2^n)/3-(3^n - 2^n))/2 for n in range(2, 22)] # Zerinvary Lajos, Jun 05 2009 (PARI) Vec(1/((1-2*x)*(1-3*x)*(1-5*x))+O(x^99)) \\ Charles R Greathouse IV, Sep 26 2012 CROSSREFS Column k=3 of A343751. Sequence in context: A026988 A081280 A038806 * A128737 A320228 A130548 Adjacent sequences: A016270 A016271 A016272 * A016274 A016275 A016276 KEYWORD nonn,easy AUTHOR STATUS approved

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Last modified March 22 09:08 EDT 2023. Contains 361423 sequences. (Running on oeis4.)