Problem 54740. Count the ways to make Scorigami

Regarding the sport known as American football, some people are such rabid fans that they can tell you the statistics of every player on their favorite team, whereas other people couldn’t tell you the winners of the last three Super Bowls.*
But one aspect of the game that everyone can enjoy is Scorigami. Devised by sportswriter Jon Bois, Scorigami is “the art of building final scores that have never happened before” in the history of the National Football League. It relies on the game’s rules of scoring:
  • 2 points for a safety
  • 3 points for a field goal
  • 6 points for a touchdown and no points after
  • 7 points for a touchdown and a kicked point after touchdown
  • 8 points for a touchdown and two-point conversion
Because a two-point conversion is uncommon and safeties are rarer still, some final scores, such as 20-17 and 27-24, have occurred many times (274 and 224, respectively, as of datenum 738683), whereas other scores, such as 19-5 and 27-18, have occurred only once and scores such as 9-8 and 25-10 have not occurred at all.
Write a function to count the ways to construct a final score, specified by two inputs W and L. Ignore the order of the scoring plays (e.g., a field goal and a touchdown would count the same as a touchdown and a field goal). For example, the score 6-3 can be made 3 ways: the losing team has a field goal, and the winning team has three safeties, two field goals, or one touchdown with no points after. The score 14-7 can be made 22 ways.
An idea for a future problem is to account for the frequency of the various scoring plays and compute the probability of a final score occurring.
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*It doesn’t matter.
from nflscorigami.com (datenum 738683)
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Solution Stats

100.0% Correct | 0.0% Incorrect
Last Solution submitted on Jun 13, 2022

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