Triangular numbers

Triangular numbers are numbers that are the counts of objects arranged in an equilateral triangle. It can be calculated as ${\binom {n+1}{2}}$, ${\frac {n(n+1)}{2}}$, or $1+2+\dots +n$. The sequence is as such:

0, 1, 3, 6, 10, 15, 21, 28, 36, 45, 55, 66, 78, 91, 105...

Visualized, that is:

            +0 = 0
     o      +1 = 1
    o o     +2 = 3
   o o o    +3 = 6
  o o o o   +4 = 10
 o o o o o  +5 = 15
o o o o o o +6 = 21 = 6(6+1)/2
                    = 6(7  )/2
                    = 42    /2
                    = 21

Implementations

AEL

40?0 0 2d[$1+!+!]m#

Counting

Outputs in unary.

when cnt == 0
  read acc
when cnt <= acc
  out "*" * cnt
when cnt > acc
  halt
   
% 1 + 2 + ... + acc

DeBruijn

Uses the fixed-point "Y" combinator to recursively find the sum of the first n naturals. The definition of f is used as example input.

(F \\0 )
(T \\1 )
(S \\\1(210) )
(f S(S(S(S(SF)))) )
(P \\\021 )
(- \0(\(\P(1F)(S(1F)))\0)(PFF)T )
(Z \0(\0FF)T )
(Y \(\1(00))[\1(00)] )

Y\\Z0[F][1(-0)S0]

> debruijn example.txt f
rem: λ λ 1 (1 (1 (1 (1 (1 (1 (1 (1 (1 (1 (1 (1 (1 (1 0))))))))))))))

Free2Edit

+5+5wsr1onl1r2+1l2r1+cl1ocwe

Iterate

(*)∞<
  *n<
    *~n<
      (1*)<>
    >
    !
  >
  (4*)1<
    (2*)=1<
      *~n< &2 >
      @
      !4
    >
    (3*)48<
      *~n< &3 >
      ~@
    >
  >
  (5*)10<
    *~n< &5 >
    ~@
  >
>

Swordfish

1~[0,,,,,v
]+#~500$%\
1]+~[@,,,\