A016296 - OEIS

%I #33 Feb 08 2025 16:04:54

%S 1,14,137,1162,9165,69342,511393,3709874,26619989,189594790,

%T 1343438889,9485451066,66805055773,469669890158,3297861746225,

%U 23135894831938,162205576930917,1136710604184246,7963332057891001,55775113548767690,390584740560075821,2734887912516137854

%N Expansion of g.f. 1/((1 - 2*x)*(1 - 5*x)*(1 - 7*x)).

%H Michael De Vlieger, <a href="/A016296/b016296.txt">Table of n, a(n) for n = 0..1182</a>

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (14,-59,70).

%F a(n-2) = ((7^n - 2^n)/5 - (5^n - 2^n)/3)/2. - _Zerinvary Lajos_, Jun 05 2009

%F From _Vincenzo Librandi_, Mar 16 2011: (Start)

%F a(n) = 14*a(n-1) - 59*a(n-2) + 70*a(n-3), n >= 3.

%F a(n) = 12*a(n-1) - 35*a(n-2) + 2^n, n >= 2. (End)

%F E.g.f.: exp(2*x)*(8 - 125*exp(3*x) + 147*exp(5*x))/30. - _Stefano Spezia_, Feb 08 2025

%t CoefficientList[Series[1/((1 - 2 x) (1 - 5 x) (1 - 7 x)), {x, 0, 18}], x] (* _Michael De Vlieger_, Jan 31 2018 *)

%t LinearRecurrence[{14,-59,70},{1,14,137},30] (* _Harvey P. Dale_, Aug 11 2021 *)

%o (Sage) [((7^n - 2^n)/5-(5^n - 2^n)/3)/2 for n in range(2,21)] # _Zerinvary Lajos_, Jun 05 2009

%K nonn,easy,changed

%O 0,2

%A _N. J. A. Sloane_