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))!.

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

Offset: 2

Author

Roger L. Bagula, Nov 09 2003

Keywords

• nonn
• less

Links

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

Crossrefs

Cf. A254864, A088488.

Programs

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}]

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)))))))

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))!.

Extensions

Edited by Antti Karttunen, Feb 09 2015