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Difference in size between rooted trees which are encoded as Matula-Goebel numbers A245821(n) and n: a(n) = A061775(A245821(n)) - A061775(n).
3

%I #12 Aug 18 2014 00:52:48

%S 0,0,0,0,0,1,0,0,-1,0,0,1,1,4,0,0,0,1,0,4,1,1,-1,0,-2,1,-1,1,0,1,0,4,

%T -2,0,1,0,1,2,-1,1,1,2,4,1,0,3,0,0,1,-2,2,-1,0,-1,-2,1,2,0,0,1,1,3,0,

%U 0,0,-1,0,5,0,-2,4,2,1,3,0,0,-1,3,1,1,0,5,-1,1,-1,2,1,1,0,4,-1,0,-2,0,3,5,-2,-1,0

%N Difference in size between rooted trees which are encoded as Matula-Goebel numbers A245821(n) and n: a(n) = A061775(A245821(n)) - A061775(n).

%H Antti Karttunen, <a href="/A245817/b245817.txt">Table of n, a(n) for n = 1..10001</a>

%F a(n) = A061775(A245821(n)) - A061775(n).

%F Other identities. For all n >= 1, the following holds:

%F a(A000040(n)) = a(n). [The result for the n-th prime is same as for n itself].

%F a(A245823(n)) = 0. [A245823 gives a (proper) subsequence of the positions of the zeros].

%o (PARI)

%o \\ Execute first the code given in A061775 and A245821.

%o A245817(n) = A061775(A245821(n)) - A061775(n);

%o for(n=1, 10001, write("b245817.txt", n, " ", A245817(n)));

%o (Scheme) (define (A245817 n) (- (A061775 (A245821 n)) (A061775 n)))

%Y Cf. A000040, A061775, A245818, A245821, A245823.

%K sign

%O 1,14

%A _Antti Karttunen_, Aug 16 2014