A016212 - OEIS

%I #23 Feb 15 2021 16:26:40

%S 1,11,90,670,4811,34041,239380,1678940,11762421,82366471,576653870,

%T 4036842810,28258696831,197813269301,1384700059560,9692921940280,

%U 67850518152041,474953820774531,3324677326552450,23272743029259350,162909206434992051,1140364460735474161

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

%H Matthew House, <a href="/A016212/b016212.txt">Table of n, a(n) for n = 0..1177</a>

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (11,-31,21).

%F a(0)=1, a(1)=11, a(n) = 10*a(n-1) - 21*a(n-2) + 1. - _Vincenzo Librandi_, Feb 10 2011

%F a(n) = (7^(n+2) - 3^(n+3) + 2)/24. - _Yahia Kahloune_, May 06 2013

%F a(n) = 11*a(n-1) - 31*a(n-2) + 21*a(n-3). - _Matthew House_, Jan 13 2017

%p a:=n->sum((7^(n-j)-3^(n-j))/4,j=0..n): seq(a(n), n=1..19); # _Zerinvary Lajos_, Jan 15 2007

%o (PARI) Vec(1/((1-x)*(1-3*x)*(1-7*x))+O(x^99)) \\ _Charles R Greathouse IV_, Sep 26 2012

%K nonn,easy

%O 0,2

%A _N. J. A. Sloane_