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%I #31 Sep 08 2022 08:44:45
%S 1,12,97,672,4333,26964,164809,998184,6017605,36192156,217414561,
%T 1305276336,7834033117,47011340388,282089500153,1692601439928,
%U 10155802087669,60935393132460,365614101138385
%N Expansion of 1/((1-x)*(1-2*x)*(1-3*x)*(1-6*x)).
%C a(n) is the area of the (n+3)-gon with vertices (2^k,3^k) for 0 <= k <= n+2). - _J. M. Bergot_ and _Robert Israel_, Dec 05 2020
%H Vincenzo Librandi, <a href="/A021029/b021029.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (12,-47,72,-36).
%F G.f.: 1/((1-x)*(1-2*x)*(1-3*x)*(1-6*x)).
%F a(n) = (-1+5*2^(n+2)-5*3^(n+2)+6^(n+2))/10. - _Bruno Berselli_, Sep 02 2011
%p seq(-1/10 + 2^(n+1) - (9*3^n)/2 + (18*6^n)/5,n=0..40); # _Robert Israel_, Dec 05 2020
%t CoefficientList[Series[1/((1 - x)(1 - 2x)(1 - 3x)(1 - 6x)), {x, 0, 30}], x] (* _Harvey P. Dale_, Mar 14 2011 *)
%o (Magma) [(-1+5*2^(n+2)-5*3^(n+2)+6^(n+2))/10: n in [0..20]]; // _Vincenzo Librandi_, Sep 02 2011
%Y Cf. A001240 (first differences).
%K nonn,easy
%O 0,2
%A _N. J. A. Sloane_
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