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URL: https://oeis.org/A016138

⇱ A016138 - OEIS

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A016138
Expansion of 1/((1-3*x)*(1-7*x)).
5
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
0,2
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
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 *)
PROG
(SageMath) [lucas_number1(n, 10, 21) for n in range(1, 30)] # Zerinvary Lajos, Apr 26 2009
(Magma) [(7^(n+1)-3^(n+1))/4: n in [0..30]]; // 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 * A388202 A006329 A077245
KEYWORD
nonn,easy
STATUS
approved