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A088487 a(n) = Sum_{k=1..8} floor(A254864(n,k)/A254864(n-1,k)), where A254864(n,k) = n! / (n-floor(n/3^k))!. 6


%S 8,10,8,8,13,8,8,24,8,8,19,8,8,22,8,8,42,8,8,28,8,8,31,8,8,86,8,8,37,

%T 8,8,40,8,8,78,8,8,46,8,8,49,8,8,96,8,8,55,8,8,58,8,8,167,8,8,64,8,8,

%U 67,8,8,132,8,8,73,8,8,76,8,8,150,8,8,82,8,8,85,8,8,328,8,8,91,8,8,94,8,8

%N a(n) = Sum_{k=1..8} floor(A254864(n,k)/A254864(n-1,k)), where A254864(n,k) = n! / (n-floor(n/3^k))!.

%C A self-similar Sierpinski-type chaotic sequence with rate three at eight levels. [The original name of the sequence.]

%C A true fractal has an infinite number of levels, but usually only six are visible.

%H Antti Karttunen, <a href="/A088487/b088487.txt">Table of n, a(n) for n = 2..10000</a>

%F a(n) = Sum_{k=1..8} floor(A254864(n,k)/A254864(n-1,k)), where A254864(n,k) = n! / (n-floor(n/3^k))!.

%t p[n_, k_]=n!/Product[i, {i, 1, n-Floor[n/3^k]}] digits=200 f[n_]=Sum[Floor[p[n, k]/p[n-1, k]], {k, 1, 8}] at=Table[f[n], {n, 2, digits}]

%o (PARI)

%o A254864bi(n,k) = prod(i=(1+(n-(n\(3^k)))),n,i);

%o A088487(n) = sum(k=1,8,(A254864bi(n,k)\A254864bi(n-1,k)));

%o for(n=2, 10000, write("b088487.txt", n, " ", A088487(n)));

%o (Scheme)

%o (define (A088487 n) (add (lambda (k) (floor->exact (/ (A254864bi n k) (A254864bi (- n 1) k)))) 1 8)) ;; Code for A254864bi given in A254864.

%o ;; The following function implements sum_{i=lowlim..uplim} intfun(i)

%o (define (add intfun lowlim uplim) (let sumloop ((i lowlim) (res 0)) (cond ((> i uplim) res) (else (sumloop (1+ i) (+ res (intfun i)))))))

%Y Cf. A254864, A088488.

%K nonn

%O 2,1

%A _Roger L. Bagula_, Nov 09 2003

%E Edited by _Antti Karttunen_, Feb 09 2015

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Last modified August 19 16:24 EDT 2017. Contains 290809 sequences.