.
(1) Go to this web-site
https://www.wolframalpha.com/input/?i=interpolating+polynomial+calculator
(2) There is free of charge "interpolating polynomial calculator" there.
Input your sequence in a specialized window there.
Press the "Compute" button.
(3) Get an approximation polynomial.
(4) This polynomial reproduces your numbers.
To guarantee that the output numbers are integer, round the polynomial output to the closest integer number every time.
(5) You can consider it as your desired "pattern" /(one of possible "rule").