(50g) Delannoy numbers - Printable Version +- HP Forums (https://www.hpmuseum.org/forum) +-- Forum: HP Software Libraries (/forum-10.html) +--- Forum: General Software Library (/forum-13.html) +--- Thread: (50g) Delannoy numbers (/thread-13063.html) (50g) Delannoy numbers - John Keith - 06-02-2019 11:34 PM Delannoy numbers have many applications in combinatorics and number theory. Fortunately they are fast and easy to compute. Further details here. The following program returns a rectangular array of Delannoy numbers. Given two integers referred to as m and n in the linked article, the program will return an array of m columns and n rows. The program actually returns a list of lists, and may be followed by AXL if a matrix is desired. The program requires the GoferLists library. Code: \<< \-> m n   \<< 1 m NDUPN \->LIST 2 n     START DUP 2.       \<< +       \>> DOSUBS 1       \<< +       \>> Scanl     NEXT n \->LIST   \>> \>> The next program returns the Delannoy triangle, also known as the tribonacci triangle. The numbers are the same as in the array but arranged in a triangle. Given an integer n, the program returns rows 0 through n of the triangle as a list of lists. Code: \<< \-> n   \<< { 1 } DUP 1 + 2 n     START DUP2 2.       \<< +       \>> DOSUBS ADD 1 + 1 SWAP +     NEXT n 1 + \->LIST   \>> \>> Finally, a program that computes the central Delannoy numbers which are the central column of the triangle and the main diagonal of the array. Given an integer n the program returns terms 0 through n of the sequence. Code: \<< \-> n   \<< 1 3 2 n     FOR k DUP2 k 6 * 3 - * SWAP k 1 - * - k /     NEXT n 1 + \->LIST   \>> \>> The last two programs will run on the HP-48G but are of limited usefulness since the numbers involved grow rapidly beyond 12 digits. RE: (50g) Delannoy numbers - Luigi Vampa - 06-03-2019 06:52 PM I never heard of Delannoy numbers. Thanks for sharing John.