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%I #12 Sep 08 2022 08:45:29
%S 1,120,524268,140737488355280,2596148429267413814265248164609936,
%T 57896044618658097711785492504343953926634992332820282019728792003956564819712
%N Eulerian numbers A000295 appearing in the intersection of Fibonacci and Lucas sequences A124168 and A127208.
%C a(n) is common to the r-step Fibonacci sequence and the s-step Lucas sequence for s=A001792(n)-2 and r=s-n+1. See A127208 for more information about the intersection of Fibonacci and Lucas sequences.
%H Vincenzo Librandi, <a href="/A127232/b127232.txt">Table of n, a(n) for n = 1..8</a> (shortened by _N. J. A. Sloane_, Jan 13 2019)
%F a(n) = 2^(k-1)-k for k=A001792(n).
%e a(2)=120 appears in the 5-step Fibonacci sequence A001591 and the 6-step Lucas sequence A074584. a(3)=524268 appears in the 16-step Fibonacci sequence and the 18-step Lucas sequence.
%o (Magma) [2^((n+2)*2^(n-1)-1)-(n+2)*2^(n-1): n in [1..7]]; // _Vincenzo Librandi_, Aug 26 2011
%o (PARI) a(n) = my(k=(n+2)*2^(n-1)); 2^(k-1)-k; \\ _Michel Marcus_, Mar 25 2016
%Y Cf. A000295, A001591, A074584, A124168, A127208.
%K nonn
%O 1,2
%A _T. D. Noe_, Jan 09 2007
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