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%I #16 Nov 15 2023 13:13:44
%S 4,7,19,67,259,1027,4099,16387,65539,262147,1048579,4194307,16777219,
%T 67108867,268435459,1073741827,4294967299,17179869187,68719476739,
%U 274877906947,1099511627779,4398046511107,17592186044419,70368744177667,281474976710659
%N a(n) = 4^n + 3.
%C Subsequence of A226807.
%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (5,-4).
%F G.f.: (4 - 13*x)/((1 - x)*(1 - 4*x)).
%F a(n) = 5*a(n-1) - 4*a(n-2) for n > 1.
%F From _Elmo R. Oliveira_, Nov 14 2023: (Start)
%F a(n) = 4*a(n-1) - 9 with a(0) = 4.
%F E.g.f.: exp(4*x) + 3*exp(x). (End)
%t Table[4^n + 3, {n, 0, 30}] (* or *) CoefficientList[Series[(4 - 13 x) / ((1 - x) (1 - 4 x)), {x, 0, 40}], x]
%o (Magma) [4^n+3: n in [0..30]];
%o (PARI) a(n)=4^n+3 \\ _Charles R Greathouse IV_, Oct 07 2015
%Y Cf. A141725, A226807.
%Y Cf. Numbers of the form k^n+k-1: A000057 (k=2), A168607 (k=3), this sequence (k=4), A242329 (k=5), A253209 (k=6), A253210 (k=7), A253211 (k=8), A253212 (k=9), A253213 (k=10).
%K nonn,easy
%O 0,1
%A _Vincenzo Librandi_, Dec 29 2014