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%I #19 Sep 08 2017 03:07:33
%S 6,42,114,222,366,546,762,1014,1302,1626,1986,2382,2814,3282,3786,
%T 4326,4902,5514,6162,6846,7566,8322,9114,9942,10806,11706,12642,13614,
%U 14622,15666,16746,17862,19014,20202,21426,22686,23982,25314
%N 6 times centered hexagonal numbers: 18*n*(n+1) + 6.
%H Harvey P. Dale, <a href="/A164016/b164016.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F a(n) = A003215(n)*6.
%F a(n) = a(n-1) + 36*n (with a(0)=6). - _Vincenzo Librandi_, Nov 30 2010
%F a(n) = 3*a(n-1)-3*a(n-2)+a(n-3) with a(0)=6, a(1)=42, a(2)=114. - _Harvey P. Dale_, Dec 16 2012
%F From _G. C. Greubel_, Sep 07 2017: (Start)
%F G.f.: 6*(1 + 4*x + x^2)/(1 - x)^3.
%F E.g.f.: 6*(1 + 6*x + 3*x^2)*exp(x). (End)
%t Table[18n(n+1)+6,{n,0,40}] (* or *) LinearRecurrence[{3,-3,1},{6,42,114},40] (* _Harvey P. Dale_, Dec 16 2012 *)
%o (PARI) a(n)=18*n*(n+1)+6 \\ _Charles R Greathouse IV_, Jul 17 2011
%Y Cf. A003215, A152746, A164013, A108099, A164015.
%K easy,nonn
%O 0,1
%A _Omar E. Pol_, Nov 07 2009
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