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 A060500 a(n) = number of drops in the n-th permutation of list A060118; the average of digits (where "digits" may eventually obtain also any values > 9) in each siteswap pattern A060496(n). 4
 0, 1, 1, 1, 1, 2, 1, 2, 1, 1, 1, 2, 1, 1, 2, 2, 2, 2, 1, 2, 2, 2, 2, 3, 1, 2, 2, 2, 2, 3, 1, 2, 1, 1, 1, 2, 1, 1, 2, 2, 2, 2, 1, 2, 2, 2, 2, 3, 1, 2, 1, 1, 1, 2, 2, 3, 2, 2, 2, 3, 2, 2, 2, 2, 2, 2, 2, 3, 2, 2, 2, 3, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 2, 2, 3, 3, 3, 3, 1, 2, 2, 2, 2, 3, 2, 3, 2 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,6 LINKS Antti Karttunen, Table of n, a(n) for n = 0..40320 FORMULA From Antti Karttunen, Aug 18 2016: (Start) The following formula reflects the original definition of computing the average, with a few unnecessary steps eliminated: a(n) = 1/s * Sum_{i=1..s} ((i-p[i]) modulo s), where p is the permutation of rank n as ordered in the list A060117, and s is its size (the number of its elements) computed as s = 1+A084558(n). a(n) = 1/s * Sum_{i=1..s} ((p[i]-i) modulo s). [If inverse permutations from list A060118 are used, then we just flip the order of difference that is used in the first formula]. a(n) = Sum_{i=1..s} [p[i] (convert(a, `+`)/nops(a)); PROG (Scheme) (define (A060500 n) (let ((s (+ 1 (A084558 n))) (p (A060118permvec-short n))) (let loop ((d 0) (i 1)) (if (> i s) d (loop (+ d (if (< (vector-ref p (- i 1)) i) 1 0)) (+ 1 i)))))) (define (A060118permvec-short rank) (permute-A060118 (make-initialized-vector (+ 1 (A084558 rank)) 1+) (+ 1 (A084558 rank)) rank)) (define (permute-A060118 elems size permrank) (let ((p (vector-head elems size))) (let unrankA060118 ((r permrank) (i 1)) (cond ((zero? r) p) (else (let* ((j (1+ i)) (m (modulo r j))) (cond ((not (zero? m)) (let ((org-i (vector-ref p i))) (vector-set! p i (vector-ref p (- i m))) (vector-set! p (- i m) org-i)))) (unrankA060118 (/ (- r m) j) j))))))) CROSSREFS Cf. A060125, A060129, A060501, A060502, A275849, A275851. Sequence in context: A219157 A080215 A266871 * A187284 A160198 A207709 Adjacent sequences:  A060497 A060498 A060499 * A060501 A060502 A060503 KEYWORD nonn AUTHOR Antti Karttunen, Mar 22 2001 EXTENSIONS Maple code collected together, alternative definition and new formulas added by Antti Karttunen, Aug 24 2016 STATUS approved

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Last modified October 21 19:58 EDT 2019. Contains 328315 sequences. (Running on oeis4.)