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

1,2

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.)

Links

Table of n, a(n) for n=1..37.

Example

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.

Prog

(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
(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

Crossrefs

Cf. A309777.

Sequence in context: A152771 A325711 A306676 * A341122 A237825 A194939

Adjacent sequences: A363055 A363056 A363057 * A363059 A363060 A363061

Keyword

nonn,fini,full

Author

Jud McCranie, May 16 2023

Status

approved