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%I #54 Sep 08 2022 08:46:07
%S 7,127,2047,32767,524287,8388607,134217727,2147483647,34359738367,
%T 549755813887,8796093022207,140737488355327,2251799813685247,
%U 36028797018963967,576460752303423487,9223372036854775807,147573952589676412927,2361183241434822606847,37778931862957161709567
%N a(n) = 2^(4*n+3) - 1.
%H Jens Kruse Andersen, <a href="/A241955/b241955.txt">Table of n, a(n) for n = 0..100</a>
%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (17,-16).
%F a(n) = 2^(4*n+3) - 1 = A000225(4*n+3) = A013777(n) - 1 = 4*A241888(n) + 3.
%F _Colin Barker_, Aug 11 2014: (Start)
%F a(n) = 17*a(n-1) - 16*a(n-2).
%F G.f.: (8*x+7) / ((x-1)*(16*x-1)). (End)
%p A241955:=n->2^(4*n+3)-1: seq(A241955(n), n=0..20); # _Wesley Ivan Hurt_, Aug 15 2014
%t Table[2^(4n + 3) - 1, {n, 0, 29}]
%t 2^(4 Range[0, 20] + 3) - 1 (* _Wesley Ivan Hurt_, Aug 15 2014 *)
%o (PARI) vector(40, n, 2^(4*n-1)-1) \\ _Derek Orr_, Aug 11 2014
%o (PARI) Vec((8*x+7)/((x-1)*(16*x-1)) + O(x^100)) \\ _Colin Barker_, Aug 11 2014
%o (Magma) [2^(4*n+3)-1 : n in [0..20]]; // _Wesley Ivan Hurt_, Aug 15 2014
%Y Cf. A000225, A004171, A013777.
%K nonn,easy
%O 0,1
%A _Wassan Letourneur_, Aug 09 2014
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