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A257971 First differences of A006921.

%I A257971 #12 Jun 20 2022 13:16:23
%S A257971 0,2,-1,5,-2,8,-5,21,-8,34,-21,81,-34,128,-81,337,-128,546,-337,1301,
%T A257971 -546,2056,-1301,5381,-2056,8706,-5381,20737,-8706,32768,-20737,86273,
%U A257971 -32768,139778,-86273,333061,-139778,526344,-333061,1377557,-526344,2228770
%N A257971 First differences of A006921.
%H A257971 Reinhard Zumkeller, <a href="/A257971/b257971.txt">Table of n, a(n) for n = 0..1000</a>
%F A257971 a(2*n) = - A168081(n), a(2*n+1) = A168081(n+2);
%F A257971 a(2*n+4) = - a(2*n+1).
%o A257971 (Haskell)
%o A257971 a257971 n = a257971_list !! n
%o A257971 a257971_list = zipWith (-) (tail a006921_list) a006921_list
%o A257971 (Python)
%o A257971 def A257971(n): return sum(int(not r & ~(n+2-r))*2**(n//2+1-r) for r in range(n//2+2)) if n & 1 else -sum(int(not r & ~(n-1-r))*2**(n//2-1-r) for r in range(n//2)) # _Chai Wah Wu_, Jun 20 2022
%Y A257971 Cf. A006911, A168081.
%K A257971 sign
%O A257971 0,2
%A A257971 _Reinhard Zumkeller_, Jul 14 2015