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+--- Thread: (49g 50g) Narayana Transform (/thread-14401.html)
(49g 50g) Narayana Transform - John Keith - 01-22-2020 10:48 PM
This program computes the Narayana transform of a list of integers. The Narayana transform is a variation of the binomial transform. Examples can be found by searching for "narayana transform" on http://oeis.org/.
This program employs an updated version of the ConvOffs transform explained in this post.
Code:
\<< DUP SIZE \-> n
\<< DUP 1. 2. SUB EVAL OVER + ROT n 1. - R\->I LSEQ :: + Scanl1 3. n
FOR k 1 OVER 1. k 1. - SUB DUP REV 2.
\<< PICK3 * SWAP /
\>> DOLIST + PICK3 1. k SUB * \GSLIST UNROT
NEXT DROP2 n \->LIST
\>>
\>>Next, the inverse Narayana transform:
Code:
\<< DUP SIZE \-> b n
\<< b 1. 2. SUB EVAL OVER - 2 2 n 1. -
R\->I LASEQ 0 :: + Scanl { -1 1 } 3. n
FOR k OVER k GET * OVER 2. k SUB / DUP \GSLIST
NEG SWAP + DUP b 1. k SUB * \GSLIST UNROT
NEXT DROP2 n \->LIST
\>>
\>>Both programs require the ListExt and GoferLists libraries.