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A330246 a(n) = 4^(n+1) + (4^n-1)/3.

%I A330246 #47 Sep 08 2022 08:46:24
%S A330246 4,17,69,277,1109,4437,17749,70997,283989,1135957,4543829,18175317,
%T A330246 72701269,290805077,1163220309,4652881237,18611524949,74446099797,
%U A330246 297784399189,1191137596757,4764550387029,19058201548117,76232806192469,304931224769877,1219724899079509
%N A330246 a(n) = 4^(n+1) + (4^n-1)/3.
%C A330246 After 4, these numbers are the third column of the rectangular array in A238475.
%H A330246 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (5,-4).
%H A330246 <a href="/index/3#3x1">Index entries for sequences related to 3x+1 (or Collatz) problem</a>
%F A330246 G.f.: (4 - 3*x) / ((1 - x)*(1 - 4*x)).
%F A330246 a(n) = 5*a(n-1) - 4*a(n-2) for n > 1.
%F A330246 a(n) = 4*a(n-1) + 1 for n > 0.
%F A330246 a(n) = (13*4^n -1)/3, for n >= 0. - _Wolfdieter Lang_, Sep 16 2021
%F A330246 a(n) = A178415(5, n) = A347834(7, n-1), arrays, for n >= 1. - _Wolfdieter Lang_, Nov 29 2021
%t A330246 Table[(4^(n + 1) + (4^n - 1) / 3), {n, 0, 30}]
%o A330246 (Magma) [4^(n+1)+(4^n-1)/3: n in [0..30]];
%Y A330246 Similar to A272743.
%Y A330246 Cf. A000302, A002450, A052909, A178415, A237930, A238475, A347834.
%Y A330246 Together with 1: first bisection of A136326.
%K A330246 nonn,easy
%O A330246 0,1
%A A330246 _Vincenzo Librandi_, Jan 09 2020