A016273 Expansion of g.f. 1/((1-2x)(1-3x)(1-5x)).

1, 10, 69, 410, 2261, 11970, 61909, 315850, 1598421, 8050130, 40425749, 202656090, 1014866581, 5079099490, 25409813589, 127092049130, 635589254741, 3178333432050, 15892828897429, 79467630222970, 397348609370901, 1986774423719810, 9933966253389269

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Links

• Index entries for linear recurrences with constant coefficients, signature (10,-31,30).

Crossrefs

Column k=3 of A343751.

Programs

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 *)

PARI

Vec(1/((1-2*x)*(1-3*x)*(1-5*x))+O(x^99)) \\ Charles R Greathouse IV, Sep 26 2012

Sage

[((5^n - 2^n)/3-(3^n - 2^n))/2 for n in range(2,22)] # Zerinvary Lajos, Jun 05 2009

Formula

From Hieronymus Fischer, Jun 25 2007: (Start)

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

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)

E.g.f.: exp(2*x)*(8 - 27*exp(x) + 25*exp(3*x))/6. - Stefano Spezia, Sep 27 2023