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A169727 a(n) = 3*(2^(n+1)-2)*(2^(n+1)-1) + 1.

%I A169727 #25 Sep 08 2022 08:45:49
%S A169727 1,19,127,631,2791,11719,48007,194311,781831,3136519,12564487,
%T A169727 50294791,201252871,805158919,3220930567,12884312071,51538427911,
%U A169727 206156070919,824629002247,3298525446151,13194120658951,52776520384519,211106157035527,844424779137031
%N A169727 a(n) = 3*(2^(n+1)-2)*(2^(n+1)-1) + 1.
%C A169727 A subsequence of the centered hexagonal numbers A003215.
%H A169727 Vincenzo Librandi, <a href="/A169727/b169727.txt">Table of n, a(n) for n = 0..1000</a>
%H A169727 Alice V. Kleeva, <a href="/A169727/a169727a.jpg">Grid for this sequence</a>
%H A169727 Alice V. Kleeva, <a href="/A169727/a169727b.jpg">Illustration of initial terms</a>
%H A169727 Robert Munafo, <a href="http://www.mrob.com/pub/math/seq-a169720.html">Sequence A169720, and two others by Alice V. Kleeva</a>
%H A169727 Robert Munafo, <a href="/A169720/a169720.pdf">Sequence A169720, and two others by Alice V. Kleeva</a> [Cached copy, in pdf format, included with permission]
%H A169727 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (7,-14,8).
%F A169727 From _R. J. Mathar_, Apr 26 2010: (Start)
%F A169727 a(n) = 7*a(n-1) - 14*a(n-2) + 8*a(n-3).
%F A169727 G.f.: -(1+12*x+8*x^2) / ( (x-1)*(2*x-1)*(4*x-1) ). (End)
%t A169727 CoefficientList[Series[-(1 + 12*x + 8*x^2)/((x-1)*(2*x-1)*(4*x-1)), {x, 0, 30}], x](* _Vincenzo Librandi_, Dec 03 2012 *)
%t A169727 LinearRecurrence[{7,-14,8},{1,19,127},30] (* _Harvey P. Dale_, Jan 15 2015 *)
%o A169727 (Magma) I:=[1, 19, 127]; [n le 3 select I[n] else 7*Self(n-1) -14*Self(n-2) +8*Self(n-3): n in [1..30]]; // _Vincenzo Librandi_, Dec 03 2012
%Y A169727 Cf. A169720-A169726, A000225.
%K A169727 nonn,easy
%O A169727 0,2
%A A169727 Alice V. Kleeva (alice27353(AT)gmail.com), Jan 19 2010
%E A169727 G.f. adapted to the offset by _Vincenzo Librandi_, Dec 03 2012