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Expansion of 1/((1-2x)(1-3x)(1-7x)).
0

%I #18 Sep 04 2017 04:16:24

%S 1,12,103,786,5713,40656,286651,2012862,14109205,98822460,691932319,

%T 4844053578,33909961177,237374494824,1661635779907,11631493440534,

%U 81420583092829,569944468808148,3989612443394215

%N Expansion of 1/((1-2x)(1-3x)(1-7x)).

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (12, -41, 42).

%F a(n) = 4*2^n/5 - 9*3^n/4 + 49*7^n/20. - _Antonio Alberto Olivares_, Feb 03 2010

%F From _Vincenzo Librandi_, Mar 15 2011: (Start)

%F a(n) = 12*a(n-1) - 41*a(n-2) + 42*a(n-3), n >= 3.

%F a(n) = 10*a(n-1) - 21*a(n-2) + 2^n, a(0)=1, a(1)=12.

%F (End)

%t CoefficientList[Series[1/((1-2x)(1-3x)(1-7x)),{x,0,30}],x] (* or *) LinearRecurrence[{12,-41,42},{1,12,103},30] (* _Harvey P. Dale_, Apr 28 2013 *)

%K nonn

%O 0,2

%A _N. J. A. Sloane_