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%I M0273 N0096 #25 Oct 14 2023 22:35:57
%S 1,0,-2,2,3,-4,-1,8,-1,-10,9,16,-18,-12,42,4,-58,40,82,-88,-54,188,18,
%T -248,151,354,-338,-260,760,120,-1031,574,1460,-1324,-1076,2948,542,
%U -3962,2075,5644,-4868,-4290,11035,2418,-14900,7346,21300,-17652,-16323,40442,9768,-54476,25675,78290,-62456
%N a(n) = Sum_{t=0..n} g(t)*g(n-t) where g(t) = A002121(t).
%C Arises in studying the Goldbach conjecture.
%C The last negative term appears to be a(485). - _T. D. Noe_, Dec 05 2006
%D N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H T. D. Noe, <a href="/A002122/b002122.txt">Table of n, a(n) for n = 0..1000</a>
%H P. A. MacMahon, <a href="https://academic.oup.com/plms/article-abstract/s2-23/1/290/1504148">Properties of prime numbers deduced from the calculus of symmetric functions</a>, Proc. London Math. Soc., 23 (1923), 290-316. = Coll. Papers, II, pp. 354-380. [The sequence G_n]
%H <a href="/index/Go#Goldbach">Index entries for sequences related to Goldbach conjecture</a>
%F G.f.: 1/(1+Sum_{k>0} (-x)^prime(k))^2.
%o (Haskell)
%o a002122 n = a002122_list !! n
%o a002122_list = uncurry conv $ splitAt 1 a002121_list where
%o conv xs (z:zs) = sum (zipWith (*) xs $ reverse xs) : conv (z:xs) zs
%o -- _Reinhard Zumkeller_, Mar 21 2014
%Y Cf. A002121.
%K sign
%O 0,3
%A _N. J. A. Sloane_
%E Edited by _Vladeta Jovovic_, Mar 29 2003
%E Entry revised by _N. J. A. Sloane_, Dec 04 2006
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