A209640 Global ranking function for restricted totally balanced binary strings given in A209641.

0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 2, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 5, 0, 6, 0, 0, 0, 7, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0

Offset: 0

Author

Antti Karttunen, Mar 24 2012

Keywords

• nonn

Comments

The given Scheme-program implements a ranking function for the terms of A209641, using Khayyam's triangle A007318.

Examples

			a(12)=3, as 12 occurs as the 3rd term (zero-based) in A209641.
a(14)=0, as 14 doesn't occur in A209641.
		

Crossrefs

This is an inverse function for A209641 in the sense that a(A209641(n)) = n for all n. The beginning of sequence coincides with A080300, because A209641 is a subsequence of A014486. Used to compute the permutation A209861.

Programs

Scheme

(define (A209640 n) (if (or (zero? n) (not (member_of_A209641? n))) 0 (let* ((w (/ (binwidth n) 2))) (let loop ((rank 0) (row 1) (u (- w 1)) (n (- n (A053644 n))) (i (/ (A053644 n) 2)) (first_0_found? #f)) (cond ((or (zero? row) (zero? u) (zero? n)) (+ (expt 2 (-1+ w)) rank)) ((> i n) (loop rank (- row 1) u n (/ i 2) #t)) (else (loop (+ rank (if first_0_found? (A007318tr (- (+ row u) 1) (- row 1)) (A007318tr (- w 1) (- row 1)))) (+ row 1) (- u 1) (- n i) (/ i 2) first_0_found?)))))))
(define (binwidth n) (let loop ((n n) (i 0)) (if (zero? n) i (loop (floor->exact (/ n 2)) (1+ i)))))