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A176972 a(n) = 7^n + 7*n + 1.

%I A176972 #41 Aug 19 2024 19:31:05
%S A176972 2,15,64,365,2430,16843,117692,823593,5764858,40353671,282475320,
%T A176972 1977326821,13841287286,96889010499,678223072948,4747561510049,
%U A176972 33232930569714,232630513987327,1628413597910576,11398895185373277,79792266297612142,558545864083284155,3909821048582988204
%N A176972 a(n) = 7^n + 7*n + 1.
%H A176972 Vincenzo Librandi, <a href="/A176972/b176972.txt">Table of n, a(n) for n = 0..300</a>
%H A176972 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (9,-15,7).
%F A176972 a(n) = A000420(n) + A008589(n) + 1 = A000420(n) + A016993(n).
%F A176972 a(n) = 7*a(n-1) - 42*(n-1) + 1, with n > 0. For n=5, a(5) = 7*2430 - 42*4 + 1 = 16843. - _Bruno Berselli_, May 18 2010
%F A176972 From _R. J. Mathar_, May 22 2010: (Start)
%F A176972 a(n) = 9*a(n-1) - 15*a(n-2) + 7*a(n-3).
%F A176972 G.f.: (-2 + 3*x + 41*x^2) / ((7*x-1)*(x-1)^2). (End)
%F A176972 E.g.f.: exp(x)*(1 + exp(6*x) + 7*x). - _Stefano Spezia_, Aug 19 2024
%e A176972 a(5) = 7^5 + 7*5 + 1 = 16843 is prime.
%t A176972 Table[7^n+7n+1,{n,0,20}] (* or *) LinearRecurrence[{9,-15,7},{2,15,64},20] (* _Harvey P. Dale_, Apr 17 2014 *)
%o A176972 (Magma) [7^n + 7*n + 1: n in [0..25]]; // _Vincenzo Librandi_, May 06 2011
%Y A176972 Cf. A000420, A008589, A016993, A176691, A176805, A176916.
%Y A176972 Cf. A370664.
%K A176972 easy,nonn
%O A176972 0,1
%A A176972 _Jonathan Vos Post_, Apr 29 2010