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Partial sums of A230407.
7

%I #13 Nov 14 2013 04:43:22

%S 0,-1,0,3,-2,-3,0,1,4,-1,-2,5,4,-1,-2,-7,-2,3,-2,-13,-12,-9,-20,-19,

%T -22,-19,-18,-15,-20,-21,-14,-15,-20,-21,-26,-21,-16,-21,-32,-31,-28,

%U -49,-48,-51,-54,-45,-44,-45,-50,-51,-56,-51,-46,-51,-62,-61,-58,-79

%N Partial sums of A230407.

%C The term a(n) indicates approximately the "balance" of the factorial beanstalk (cf. A219666) at n steps up from the root, which in turn correlates with the behavior of such sequences as A219662 and A219663.

%C This sequence relates to the factorial base representation (A007623) in the same way as A218789 relates to the binary system.

%C Question: When will a negative term occur next time, after a(251) = -41 ?

%H Antti Karttunen, <a href="/A230409/b230409.txt">Table of n, a(n) for n = 0..21622</a>

%F a(0) = 0, a(n) = a(n-1) + A230407(n).

%o (Scheme, with _Antti Karttunen_'s IntSeq-library)

%o (define A230409 (PARTIALSUMS 0 0 A230407))

%o ;; Alternatively, using memoization macro definec from the same library:

%o (definec (A230409 n) (if (zero? n) n (+ (A230407 n) (A230409 (- n 1)))))

%Y Cf. A230407 & A230408, A219662 & A219663.

%K sign

%O 0,4

%A _Antti Karttunen_, Nov 10 2013