A088488 a(n) = Sum_{k=1..8} floor(A254876(n,k)/A254876(n-1,k)), where A254876(n,k) = n! / (Product_{m=(n-floor((2n)/(3^k))) .. (n-floor((n)/(3^k)))} m).

8, 17, 22, 26, 40, 43, 49, 66, 65, 69, 87, 87, 68, 109, 108, 109, 137, 130, 130, 157, 153, 133, 180, 174, 171, 211, 196, 191, 227, 218, 186, 250, 240, 232, 280, 262, 253, 298, 285, 164, 319, 304, 292, 350, 327, 313, 367, 349, 292, 390, 371, 354, 426, 393, 375

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. A088487, A254876.

Programs

Mathematica

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

PARI

A088488(n) = sum(k=1,8,(A254876bi(n,k)\A254876bi(n-1,k)));
A254876bi(n,k) = n! / prod(i=(n-((2*n)\(3^k))),(n-(n\(3^k))),i);
for(n=2, 10000, write("b088488.txt", n, " ", A088488(n)));

Scheme

(define (A088488 n) (add (lambda (k) (floor->exact (/ (A254876bi n k) (A254876bi (- n 1) k)))) 1 8))
;; 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(A254876(n,k)/A254876(n-1,k)), where A254876(n,k) = n! / (Product_{m=(n-floor((2n)/(3^k))) .. (n-floor((n)/(3^k)))} m).

Extensions

Edited by Antti Karttunen, Feb 09 2015