A016138 Expansion of 1/((1-3*x)*(1-7*x)).

1, 10, 79, 580, 4141, 29230, 205339, 1439560, 10083481, 70604050, 494287399, 3460188940, 24221854021, 169554572470, 1186886790259, 8308221880720, 58157596211761, 407103302622490, 2849723505777919, 19948065702706900, 139636463405732701, 977455254300482110, 6842186811484434379, 47895307774534219480

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (10,-21).

Crossrefs

Cf. Column k=1 of A225469.

Programs

Magma

[(7^(n+1)-3^(n+1))/4: n in [0..30]]; // Vincenzo Librandi, Oct 09 2011

Mathematica

Table[(7^(n+1) - 3^(n+1))/4, {n,0,40}] (* Vladimir Joseph Stephan Orlovsky, Jan 27 2011 *)
CoefficientList[Series[1/((1-3x)(1-7x)),{x,0,30}],x] (* or *) LinearRecurrence[{10,-21},{1,10},30] (* Harvey P. Dale, Nov 07 2014 *)

PARI

Vec(1/((1-3*x)*(1-7*x))+O(x^99)) \\ Charles R Greathouse IV, Sep 26 2012

Sage

[lucas_number1(n,10,21) for n in range(1, 30)] # Zerinvary Lajos, Apr 26 2009

Formula

a(n) = (7^(n+1) - 3^(n+1))/4. - Lambert Klasen (lambert.klasen(AT)gmx.net), Feb 05 2005

a(n) = 10*a(n-1) - 21*a(n-2). - Philippe Deléham, Jan 01 2009

G.f.: x/(1-10*x+21*x^2). - Zerinvary Lajos, Apr 26 2009

E.g.f.: (d/dx)(exp(3*x)*(exp(4*x)-1)/4) = exp(3*x)*(7*exp(4*x) - 3)/4. - Wolfdieter Lang, Apr 13 2017