(50G)Integer Partitions in Fibonacci Numbers
08-12-2015, 02:34 PM (This post was last modified: 06-15-2017 01:40 PM by Gene.)
Post: #1
 Gerald H Senior Member Posts: 1,457 Joined: May 2014
(50G)Integer Partitions in Fibonacci Numbers
The total number of partitions of

7

is

15

of which

10

are composed purely of Fibonacci numbers &

1

is composed of distinct Fibonacci numbers.

{ [ 7 ] [ 6 1 ] [ 5 2 ] [ 5 1 1 ] [ 4 3 ] [ 4 2 1 ] [ 4 1 1 1 ] [ 3 3 1 ] [ 3 2 2 ] [ 3 2 1 1 ] [ 3 1 1 1 1 ] [ 2 2 2 1 ] [ 2 2 1 1 1 ] [ 2 1 1 1 1 1 ] [ 1 1 1 1 1 1 1 ] }

The programme PINFIBS returns for integer input the number of partitions in Fibonacci numbers.

Code:
 PINFIBS ::   CK1&Dispatch   BINT1   ::     "       # PARTITIONS IN FIBOS"     DispCoord1     SetDA3Temp     %ABSCOERCE     ONEONE     '     ::       3PICK3PICK       #<       case2drop       ::         #0=case         BINT1         BINT0       ;       3PICK3PICK       #-       3PICK3PICK       1GETLAM       EVAL       4UNROLL       OVER       #+SWAP       1GETLAM       EVAL       #+     ;     DUP1LAMBIND     EVAL     ABND     FPTR2 ^#>Z   ; ;

The programme PINDFIBS returns for integer input the number of partitions in distinct Fibonacci numbers.

Code:
 PINDFIBS ::   CK1&Dispatch   BINT1   ::     "  # PARTITIONS IN DISTINCT FIBOS"     DispCoord1     SetDA3Temp     %ABSCOERCE     ONEONE     '     ::       3PICK3PICK       #<       case2drop       ::         #0=case         BINT1         BINT0       ;       3PICK3PICK       #-       3PICK3PICK       OVER       #+SWAP       1GETLAM       EVAL       4UNROLL       OVER       #+SWAP       1GETLAM       EVAL       #+     ;     DUP1LAMBIND     EVAL     ABND     FPTR2 ^#>Z   ; ;
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