Fusc sequence

Write a script to generate first 50 members of the FUSC Sequence. Please refer to the OEIS for more information.

The sequence is defined as below:

• fusc(0) = 0
• fusc(1) = 1
• for n > 1, when n is:
  • even: fusc(n) = fusc(n / 2),
  • odd: fusc(n) = fusc((n-1)/2) + fusc((n+1)/2)

Examples

fusc(0) =  0
fusc(1) =  1
fusc(2) =  1
fusc(3) =  2
fusc(4) =  1 ...

Analysis

Stern's diatomic series also known as fusc, is a series of interest in the field of number theory, although I have not found any pratical use for it in the documentation.

It is easily computed using the instructions in the task statement above, and that's what I did.

I am sorry that the 'Try it' feature is currently working very slowly or not at all owing to some issue with my web hosting provider.

Try it 

#!/usr/bin/perl

# Blog: http://ccgi.campbellsmiths.force9.co.uk/challenge

use v5.26;    # The Weekly Challenge - 2021-03-15
use utf8;     # Week 104 - task 1 - Fusc sequence
use warnings; # Peter Campbell Smith
binmode STDOUT, ':utf8';
use Encode;

fusc_sequence(50);

sub fusc_sequence {

    my ($stop, @fusc);

    # initialise
    $stop = $_[0];
    
    # calculate per rules
    $fusc[0] = 0;
    $fusc[1] = 1;
    $fusc[$_] = $_ & 1 ? 
        $fusc[($_ - 1) / 2] + $fusc[($_ + 1) / 2] : 
        $fusc[$_ / 2] for 2 .. $stop - 1;

    # show results nicely
    say qq[\nInput:  $stop];
    say qq[Output: ];
    for (0 .. $stop - 1) {
        print sprintf('fusc(%2d) = %2d', $_, $fusc[$_]) . ($_ < $stop - 1 ? ', ' : '');
        say '' if ($_ + 1) % 5 == 0;
    }
}

13 lines of code
Completed after the closing date and not submitted to GitHub

Output from script

Input:  50
Output:
fusc( 0) =  0, fusc( 1) =  1, fusc( 2) =  1, fusc( 3) =  2, 
fusc( 4) =  1, fusc( 5) =  3, fusc( 6) =  2, fusc( 7) =  3, 
fusc( 8) =  1, fusc( 9) =  4, fusc(10) =  3, fusc(11) =  5, 
fusc(12) =  2, fusc(13) =  5, fusc(14) =  3, fusc(15) =  4,
fusc(16) =  1, fusc(17) =  5, fusc(18) =  4, fusc(19) =  7,
fusc(20) =  3, fusc(21) =  8, fusc(22) =  5, fusc(23) =  7,
fusc(24) =  2, fusc(25) =  7, fusc(26) =  5, fusc(27) =  8, 
fusc(28) =  3, fusc(29) =  7, fusc(30) =  4, fusc(31) =  5,
fusc(32) =  1, fusc(33) =  6, fusc(34) =  5, fusc(35) =  9,
fusc(36) =  4, fusc(37) = 11, fusc(38) =  7, fusc(39) = 10,
fusc(40) =  3, fusc(41) = 11, fusc(42) =  8, fusc(43) = 13,
fusc(44) =  5, fusc(45) = 12, fusc(46) =  7, fusc(47) =  9,
fusc(48) =  2, fusc(49) =  9