A245818 Difference in size between rooted trees which are encoded with Matula-Goebel numbers A245822(n) and n: a(n) = A061775(A245822(n)) - A061775(n).

0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 2, -1, 2, 0, 0, 1, 0, 1, 2, -1, 0, -1, 2, -1, 1, 0, -1, 0, 2, 1, 2, 1, -1, 0, 1, 1, 2, 0, 0, 2, 2, -1, -1, -1, 0, 1, -1, 1, 0, 2, -1, -1, 1, 0, 3, 0, 0, 0, 3, -1, 0, 0, 0, 1, 3, -2, 0, 0, 0, 1, 2, -1, 2, 3, 0, 2, 2, -4, 1, -1, 1, 3, 4, -1, 0, 0, -2, 1, 0, 1, 1, 0, 0, -1, 1, 1, 0

Offset: 1

Author

Antti Karttunen, Aug 16 2014

Keywords

• sign

Links

• Antti Karttunen, Table of n, a(n) for n = 1..10001

Crossrefs

Cf. A000040, A061775, A245817, A245822, A245823.

Programs

PARI

\\ Execute first the code given in A061775 and A245822.
A245818(n) = A061775(A245822(n)) - A061775(n);
for(n=1, 10001, write("b245818.txt", n, " ", A245818(n)));

Scheme

(define (A245818 n) (- (A061775 (A245822 n)) (A061775 n)))

Formula

a(n) = A061775(A245822(n)) - A061775(n).

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

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

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