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A267615 a(n) = 2^n + 11.

%I A267615 #24 Nov 08 2023 14:27:56
%S A267615 12,13,15,19,27,43,75,139,267,523,1035,2059,4107,8203,16395,32779,
%T A267615 65547,131083,262155,524299,1048587,2097163,4194315,8388619,16777227,
%U A267615 33554443,67108875,134217739,268435467,536870923,1073741835,2147483659,4294967307,8589934603,17179869195,34359738379
%N A267615 a(n) = 2^n + 11.
%C A267615 Recurrence relation b(n) = 3*b(n - 1) - 2*b(n - 2) for n>1, b(0) = k, b(1) = k + 1, gives the closed form b(n) = 2^n + k - 1.
%H A267615 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (3,-2).
%F A267615 G.f.: (12 - 23*x)/(1 - 3*x + 2*x^2).
%F A267615 a(n) = 3*a(n - 1) - 2*a(n - 2) for n>1, a(0)=12, a(1)=13.
%F A267615 a(n) = A000079(n) + A010850(n).
%F A267615 Sum_{n>=0} 1/a(n) = 0.367971714327125...
%F A267615 Lim_{n->oo} a(n + 1)/a(n) = 2.
%F A267615 E.g.f.: exp(2*x) + 11*exp(x). - _Elmo R. Oliveira_, Nov 08 2023
%t A267615 Table[2^n + 11, {n, 0, 35}]
%t A267615 LinearRecurrence[{3, -2}, {12, 13}, 40] (* _Vincenzo Librandi_, Jan 19 2016 *)
%o A267615 (PARI) a(n) = 2^n + 11; \\ _Altug Alkan_, Jan 18 2016
%o A267615 (Magma) [2^n+11: n in [0..30]]; // _Vincenzo Librandi_, Jan 19 2016
%Y A267615 Cf. sequences with closed form 2^n + k - 1: A168616 (k=-4), A028399 (k=-3), A036563 (k=-2),  A000918 (k=-1), A000225 (k=0), A000079 (k=1), A000051 (k=2), A052548 (k=3), A062709 (k=4), A140504 (k=5), A168614 (k=6), A153972 (k=7), A168415 (k=8), A242475 (k=9), A188165 (k=10), A246139 (k=11), this sequence (k=12).
%Y A267615 Cf. A156940.
%K A267615 nonn,easy
%O A267615 0,1
%A A267615 _Ilya Gutkovskiy_, Jan 18 2016