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A016273 Expansion of 1/((1-2x)(1-3x)(1-5x)). 1
1, 10, 69, 410, 2261, 11970, 61909, 315850, 1598421, 8050130, 40425749, 202656090, 1014866581, 5079099490, 25409813589, 127092049130, 635589254741, 3178333432050, 15892828897429, 79467630222970 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Table of n, a(n) for n=0..19.

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 xrange(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

Sequence in context: A026988 A081280 A038806 * A128737 A320228 A130548

Adjacent sequences:  A016270 A016271 A016272 * A016274 A016275 A016276

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane

STATUS

approved

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Last modified April 24 12:21 EDT 2019. Contains 322429 sequences. (Running on oeis4.)