A363058 Number of ways to get n points in a bridge hand.

1, 2, 3, 5, 5, 8, 9, 12, 13, 16, 17, 21, 21, 24, 25, 28, 27, 30, 29, 31, 29, 30, 27, 28, 25, 24, 21, 21, 17, 16, 13, 11, 8, 6, 3, 2, 1

Offset: 1

Author

Jud McCranie, May 16 2023

Keywords

• nonn
• fini
• full

Comments

The most common way of evaluating a bridge hand (13 cards from a standard deck) is to count a jack as 1 point, a queen as 2 points, a king as 3 points, and an ace as 4 points, and add them together. (Suits are ignored.)

Examples

			a(2)=2 because you can have a total of 2 points in two ways: two jacks or one queen, and a(3)=3 because you can have a total of 3 points in three ways: one king, one queen plus one jack, or three jacks.
		

Crossrefs

Cf. A309777.

Programs

PARI

a363058(n) = {my (c=0); for (a=0,4, for (k=0,4, for (q=0,4, for (j=0,4, if (a+k+q+j<=13 && 4*a+3*k+2*q+j==n, c++))))); c};
for (n=1,37, print1(a363058(n),", ")) \\ Hugo Pfoertner, Oct 01 2023

R

card_values <- c(
  Ace = 4,
  King = 3,
  Queen = 2,
  Jack = 1
)
combinations <- function(n) {
  count <- 0
  for (a in 0:4) {
    for (k in 0:4) {
      for (q in 0:4) {
        for (j in 0:4) {
          if (a + k + q + j <= 13 &&
              a * card_values['Ace'] + k * card_values['King'] + q * card_values['Queen'] + j * card_values['Jack'] == n) {
            count <- count + 1
          }
        }
      }
    }
  }
  return(count)
}
results_vector <- c()
for (n in 1:37) {
  output <- combinations(n)
  if (output > 0) {
    results_vector <- c(results_vector, output)
  }
}
format_output <- paste(results_vector, collapse = ", ")
cat(format_output)
# W. Kyle Hamilton, Oct 01 2023