A213704 Catalan Unranking function U(size,rank) for totally balanced binary strings (converted to decimal). Each row 'size' of an array lists all A000108(size) such items in standard lexicographic order, followed by an infinite number of zeros.

0, 0, 2, 0, 0, 10, 0, 0, 12, 42, 0, 0, 0, 44, 170, 0, 0, 0, 50, 172, 682, 0, 0, 0, 52, 178, 684, 2730, 0, 0, 0, 56, 180, 690, 2732, 10922, 0, 0, 0, 0, 184, 692, 2738, 10924, 43690, 0, 0, 0, 0, 202, 696, 2740, 10930, 43692, 174762, 0, 0, 0, 0, 204, 714, 2744, 10932, 43698, 174764, 699050, 0

Offset

0,3

Comments

The Scheme-function CatalanUnrank has been adapted from Frank Ruskey's thesis. This gives essentially the same information as A014486 which can be obtained from this array by concatenating all A000108(s) nonzero terms from the beginning of each row s to one sequence.

See the comments and pictures at A014486 for more information.

Links

Antti Karttunen, Rows n=0..54 of triangle, flattened

A. Karttunen et al., Ranking and unranking functions, OEIS Wiki.

F. Ruskey, Algorithmic Solution of Two Combinatorial Problems, Thesis, Department of Applied Physics and Information Science, University of Victoria, 1978.

Prog

(Scheme):
(define (A213704 n) (A213704bi (A002262 n) (A025581 n)))
(define (A213704bi row col) (cond ((zero? row) 0) ((>= col (A000108 row)) 0) (else (CatalanUnrank row col))))
(define (CatalanUnrank size rank) (let loop ((a 0) (m (-1+ size)) (y size) (rank rank) (c (A009766tr (-1+ size) size))) (if (negative? m) a (if (>= rank c) (loop (1+ (* 2 a)) m (-1+ y) (- rank c) (A009766tr m (-1+ y))) (loop (* 2 a) (-1+ m) y rank (A009766tr (-1+ m) y))))))

Crossrefs

The leftmost column: A020988. For all n>1, A014486(n) = A213704bi(A072643(n),(n - A014137(A072643(n)-1))). Cf. A009766, A215406, A153250.

Sequence in context: A181499 A010893 A181501 * A278099 A000171 A054922

Adjacent sequences: A213701 A213702 A213703 * A213705 A213706 A213707

Keyword

nonn,tabl

Author

Antti Karttunen, Aug 10 2012

Status

approved