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+--- Thread: (49g 50g) Bell numbers (/thread-11247.html)
(49g 50g) Bell numbers - John Keith - 08-19-2018 04:14 PM
Following on from this post, this program returns a list of the Bell numbers ( A000110 in OEIS) from 0 through n:
Code:
\<< I\->R \-> n
\<< 1 1 { 1 } 2. n
START OVER :: + Scanl DUP Last NEWOB SWAP
NEXT DROP n 1. + \->LIST
\>>
\>>A simple modification of the above will return rows 0 through n of the Bell triangle, OEIS A011971:
Code:
\<< I\->R \-> n
\<< { 1 } 1. n
START DUPDUP Last NEWOB :: + Scanl
NEXT n 1. + \->LIST
\>>
\>>Both programs require GoferLists and should be run in exact mode due to the size of the numbers involved.
These programs are adapted (i.e. shamelessly stolen) from the excellent Haskell and Python programs in the OEIS links above.
RE: (49g 50g) Bell numbers - John Keith - 03-03-2020 09:51 PM
Both programs in the post above have been replaced with new programs which are shorter, faster and use less memory. In particular, the first program can compute much longer lists of Bell numbers without an "Insufficient Memory" error.
RE: (49g 50g) Bell numbers - Gerald H - 03-04-2020 05:37 AM
For integer input N the programme returns the Nth Bell number:
Code:
Size: 117.
CkSum: # 4DCAh
::
CK1&Dispatch
# FF
::
FPTR2 ^DupZIsNeg?
caseSIZEERR
FPTR2 ^DupQIsZero?
casedrop
ZINT 1
DUP
ZINT 3
Z<
?SEMI
FPTR2 ^Z2BIN
DUP1LAMBIND
ZINT 1
SWAP
ONE_DO
DUPINDEX@
#>$
BIGDISPROW3
INDEX@
#1+_ONE_DO
DUP
JINDEX@
#2+ROLL
FPTR2 ^RADDext
LOOP
LOOP
1GETLAM
UNROLL
1GETABND
#1-
NDROP
;
;