(49G) Number of Integer Partitions in Squares

(49G) Number of Integer Partitions in Squares - Printable Version

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(49G) Number of Integer Partitions in Squares - Gerald H - 07-29-2015 10:15 AM

For integer input the programme returns the number of integer partitions in squares.

eg For input

7

the programme returns

2

& indeed

7 = 1 + 1 + 1 + 1 + 1 + 1 + 1

&

7 = 4 + 1 + 1 + 1

& these are the only two partitions purely in squares.

Similarly, for input

100

the programme returns

1,116

For more info see

http://oeis.org/A001156

Code:

::

  CK1&Dispatch

  BINT1

  ::

    %ABSCOERCE

    BINT1

    BINT3

    '

    ::

      DEPTH

      #>$

      BIGDISPROW3

      3PICK3PICK

      #<case

      ::

        2DROP

        #0=case

        BINT1

        BINT0

      ;

      3PICK3PICK

      #-

      3PICK3PICK

      1GETLAM

      EVAL

      4UNROLL

      DUPUNROT

      #+SWAP

      #2+

      1GETLAM

      EVAL

      #+

    ;

    DUP1LAMBIND

    EVAL

    ABND

    FPTR2 ^#>Z

  ;

;