Riordan numbers
Riordan numbers is a draft programming task. It is not yet considered ready to be promoted as a complete task, for reasons that should be found in its talk page.
Riordan numbers show up in several places in set theory. They are closely related to Motzkin numbers, and may be derived from them.
Riordan numbers comprise the sequence a where:
a(0) = 1, a(1) = 0, for subsequent terms, a(n) = (n-1)*(2*a(n-1) + 3*a(n-2))/(n+1)
There are other generating functions, and you are free to use one most convenient for your language.
- Task
- Find and display the first 32 Riordan numbers.
- Stretch
- Find and display the digit count of the 1000th Riordan number.
- See also
Raku
<lang perl6>use Lingua::EN::Numbers;
my @riordan = 1, 0, { state $n = 1; (++$n - 1) / ($n + 1) × (3 × $^a + 2 × $^b) } … *;
my $upto = 32; say "First {$upto.&cardinal} Riordan numbers:\n" ~ @riordan[^$upto]».&comma».fmt("%17s").batch(4).join("\n") ~ "\n"; say "The 1000th has {@riordan[9999].chars} digits"; </lang>
- Output:
First thirty-two Riordan numbers:
1 0 1 1
3 6 15 36
91 232 603 1,585
4,213 11,298 30,537 83,097
227,475 625,992 1,730,787 4,805,595
13,393,689 37,458,330 105,089,229 295,673,994
834,086,421 2,358,641,376 6,684,761,125 18,985,057,351
54,022,715,451 154,000,562,758 439,742,222,071 1,257,643,249,140
The 1000th has 4765 digits