OFFSET

0,5

COMMENTS

D. E. Knuth writes: "No simple formula seems to exist, but the listings can be counted for small s and t by systematically computing the numbers of genlex paths that run through all weight-t strings from a given starting point to a given ending point via revolving-door moves." (See reference Knuth.)

REFERENCES

D. E. Knuth, The Art of Computer Programming, Volume 4, Fascicle 3, Generating all Combinations and Partitions, Addison-Wesley 2005, section 7.2.1.3, solution to exercise 32.

EXAMPLE

1

1, 1

1, 2, 1

1, 4, 4, 1

1, 8, 20, 8, 1

1, 16, 160, 160, 16, 1

1, 32, 2264, 17152, 2264, 32, 1

CROSSREFS

KEYWORD

AUTHOR

Peter Luschny, Jan 31 2009

STATUS

approved