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%I #39 Feb 19 2024 01:53:37
%S 1,17,209,2257,22737,219345,2054353,18831569,169826513,1512003793,
%T 13323163857,116402378961,1009755576529,8706336970961,74677034637521,
%U 637626988058833,5422701592139985,45955098238474449
%N a(1)=1, a(n) = n*8^(n-1) + a(n-1).
%H Iain Fox, <a href="/A014921/b014921.txt">Table of n, a(n) for n = 1..1104</a> (first 1000 terms from Vincenzo Librandi)
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (17,-80,64).
%F G.f.: -x/((x-1)*(8*x-1)^2). - _Colin Barker_, Oct 15 2012
%F a(1)=1, a(2)=17, a(n) = 16*a(n-1) - 64*a(n-2) + 1. - _Vincenzo Librandi_, Oct 23 2012
%F E.g.f.: (exp(x) + exp(8*x)*(56*x - 1))/49. - _Iain Fox_, Aug 10 2018
%p a:=n->sum (8^n-8^j, j=0..n): seq(a(n)/7, n=1..21); # _Zerinvary Lajos_, Dec 14 2008
%t CoefficientList[Series[1/((1 - x)(1 - 8*x)^2), {x, 0, 40}], x] (* _Vincenzo Librandi_, Oct 23 2012 *)
%t a[n_] := (1 + (7 n - 1) 8^n)/49; Array[a, 19, 0] (* _Robert G. Wilson v_, Aug 10 2018 *)
%o (Magma) I:=[1, 17]; [n le 2 select I[n] else 16*Self(n-1)-64*Self(n-2)+1: n in [1..30]]; // _Vincenzo Librandi_, Oct 23 2012
%o (PARI) first(n) = my(res=vector(n)); res[1]=1; for(x=2, n, res[x]=x*8^(x-1)+res[x-1]); res \\ _Iain Fox_, Aug 10 2018
%o (PARI) a(n) = (1 + 8^n*(7*n-1))/49 \\ _Iain Fox_, Aug 10 2018
%o (PARI) first(n) = Vec(x/((1-x)*(1-8*x)^2) + O(x^(n+1))) \\ _Iain Fox_, Aug 10 2018
%o (GAP) a:=[1];; for n in [2..20] do a[n]:=n*8^(n-1)+a[n-1]; od; a; # _Muniru A Asiru_, Aug 12 2018
%K nonn,easy
%O 1,2
%A _Olivier GĂ©rard_