This site is supported by donations to The OEIS Foundation.



Annual Appeal: Please make a donation (tax deductible in USA) to keep the OEIS running. Over 5000 articles have referenced us, often saying "we discovered this result with the help of the OEIS".

(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy .

Last modified December 8 06:50 EST 2016. Contains 278902 sequences.