This jupyter notebooks implement two algorithms for counting possible covers of m x n rectangle with 1 x 2 dominoes.
This notebook contains an implementation based on Temperley, Fisher, Kasteleyn formula 🐰.
And this notebook contains a detailed explanation of a recursive algorithm aka dynamic programming approach 🔄. There is a PDF version for convenience.
https://en.wikipedia.org/wiki/Domino_tiling
https://ru.wikipedia.org/wiki/%D0%90%D0%BB%D0%B3%D0%BE%D1%80%D0%B8%D1%82%D0%BC_FKT
https://en.wikipedia.org/wiki/Packing_problems
https://elementy.ru/problems/1612/Poloski_iz_domino
http://www.dep.ufscar.br/docentes/morabito/jors98.pdf
https://www.researchgate.net/publication/233653794_An_effective_recursive_partitioning_approach_for_the_packing_of_identical_rectangles_in_a_rectangle
https://en.wikipedia.org/wiki/Domino_tiling
https://arxiv.org/pdf/math/0310326.pdf
https://www.geeksforgeeks.org/count-number-ways-tile-floor-size-n-x-m-using-1-x-m-size-tiles/
https://www.geeksforgeeks.org/tiling-problem/
https://www.geeksforgeeks.org/tiling-with-dominoes/
https://stackoverflow.com/questions/16388579/spoj-m3tile-solution-explanation
https://www.fq.math.ca/Scanned/18-1/read.pdf
https://stackoverflow.com/questions/31354624/number-of-ways-to-tile-a-w-x-h-grid-with-2-x-1-and-1-x-2-dominos
https://www.quora.com/In-how-many-ways-can-a-MxN-rectangle-be-tiled-using-1x1-and-1x2-elements
http://www.math.cmu.edu/~bwsulliv/domino-tilings.pdf
https://math.stackexchange.com/questions/664113/count-the-ways-to-fill-a-4-times-n-board-with-dominoes
http://algo.inria.fr/seminars/sem01-02/strehl.pdf
https://cp-algorithms.com/dynamic_programming/profile-dynamics.html
https://neerc.ifmo.ru/wiki/index.php?title=%D0%94%D0%B8%D0%BD%D0%B0%D0%BC%D0%B8%D1%87%D0%B5%D1%81%D0%BA%D0%BE%D0%B5_%D0%BF%D1%80%D0%BE%D0%B3%D1%80%D0%B0%D0%BC%D0%BC%D0%B8%D1%80%D0%BE%D0%B2%D0%B0%D0%BD%D0%B8%D0%B5_%D0%BF%D0%BE_%D0%BF%D1%80%D0%BE%D1%84%D0%B8%D0%BB%D1%8E
http://sk765.blogspot.com/2012/02/dynamic-programming-with-profile.html
https://blog.evilbuggy.com/2018/05/broken-profile-dynamic-programming.html
https://ru.coursera.org/lecture/sportivnoe-programmirovanie/4-5-zadacha-parkiet-dinamika-po-profiliu-k3EYK
https://habr.com/ru/post/191498/
https://archive.lksh.ru/2011/july/B/files/dp-profile.pdf