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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
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, 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, 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 (list; graph; refs; listen; history; text; internal format)
OFFSET

2,1

COMMENTS

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

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

LINKS

Antti Karttunen, Table of n, a(n) for n = 2..10000

FORMULA

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

MATHEMATICA

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}]

PROG

(PARI)

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

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

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

(Scheme)

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

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

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

CROSSREFS

Cf. A254864, A088488.

Sequence in context: A124685 A105021 A273651 * A010733 A066004 A107032

Adjacent sequences:  A088484 A088485 A088486 * A088488 A088489 A088490

KEYWORD

nonn

AUTHOR

Roger L. Bagula, Nov 09 2003

EXTENSIONS

Edited by Antti Karttunen, Feb 09 2015

STATUS

approved

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Last modified July 22 05:47 EDT 2019. Contains 325213 sequences. (Running on oeis4.)