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A205087 a(n) = n 7's sandwiched between two 1's.

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%I A205087 #27 Feb 18 2025 16:34:53
%S A205087 11,171,1771,17771,177771,1777771,17777771,177777771,1777777771,
%T A205087 17777777771,177777777771,1777777777771,17777777777771,
%U A205087 177777777777771,1777777777777771,17777777777777771,177777777777777771,1777777777777777771,17777777777777777771
%N A205087 a(n) = n 7's sandwiched between two 1's.
%H A205087 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (11,-10).
%F A205087 a(0)=1, a(n) = 10*a(n-1) + 61.
%F A205087 a(n) = (160*10^n - 61)/9 (see PARI's code by Charles R Greathouse IV).
%F A205087 From _Elmo R. Oliveira_, Feb 18 2025: (Start)
%F A205087 G.f.: (11 + 50*x)/((1 - x)*(1 - 10*x)).
%F A205087 E.g.f.: exp(x)*(160*exp(9*x) - 61)/9.
%F A205087 a(n) = 11*a(n-1) - 10*a(n-2). (End)
%t A205087 a[0]=11;a[n_]:=a[n-1]*10+61;Table[a[n],{n,0,44}]
%t A205087 Table[10 FromDigits[PadRight[{1},n,7]]+1,{n,20}] (* _Harvey P. Dale_, Nov 18 2022 *)
%o A205087 (PARI) a(n)=(160*10^n-61)/9 \\ _Charles R Greathouse IV_, Jan 23 2012
%Y A205087 Cf. A002281.
%K A205087 nonn,easy,less,base
%O A205087 0,1
%A A205087 _José María Grau Ribas_, Jan 22 2012