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

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

Offset

0,2

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (10,-21).

Formula

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

a(n) = ((5+sqrt4)^n - (5-sqrt4)^n)/4 in Fibonacci form. Offset 1. a(3)=79. - Al Hakanson (hawkuu(AT)gmail.com), Dec 31 2008

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

Mathematica

Join[{a=1, b=10}, Table[c=10*b-21*a; a=b; b=c, {n, 60}]] (* 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 *)

Prog

(Sage) [lucas_number1(n, 10, 21) for n in range(1, 20)] # Zerinvary Lajos, Apr 26 2009
(Magma) [(7^(n+1)-3^(n+1))/4: n in [0..20]]; // Vincenzo Librandi, Oct 09 2011
(PARI) Vec(1/((1-3*x)*(1-7*x))+O(x^99)) \\ Charles R Greathouse IV, Sep 26 2012

Crossrefs

Cf. Column k=1 of A225469.

Sequence in context: A006469 A288630 A081905 * A006329 A077245 A036732

Adjacent sequences: A016135 A016136 A016137 * A016139 A016140 A016141

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved