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%I #29 Oct 19 2023 06:28:00
%S 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,
%T 24,21,21,17,16,13,11,8,6,3,2,1
%N Number of ways to get n points in a bridge hand.
%C 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.)
%e 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.
%o (R)
%o card_values <- c(
%o Ace = 4,
%o King = 3,
%o Queen = 2,
%o Jack = 1
%o )
%o combinations <- function(n) {
%o count <- 0
%o for (a in 0:4) {
%o for (k in 0:4) {
%o for (q in 0:4) {
%o for (j in 0:4) {
%o if (a + k + q + j <= 13 &&
%o a * card_values['Ace'] + k * card_values['King'] + q * card_values['Queen'] + j * card_values['Jack'] == n) {
%o count <- count + 1
%o }
%o }
%o }
%o }
%o }
%o return(count)
%o }
%o results_vector <- c()
%o for (n in 1:37) {
%o output <- combinations(n)
%o if (output > 0) {
%o results_vector <- c(results_vector, output)
%o }
%o }
%o format_output <- paste(results_vector, collapse = ", ")
%o cat(format_output)
%o # _W. Kyle Hamilton_, Oct 01 2023
%o (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};
%o for (n=1,37, print1(a363058(n),", ")) \\ _Hugo Pfoertner_, Oct 01 2023
%Y Cf. A309777.
%K nonn,fini,full
%O 1,2
%A _Jud McCranie_, May 16 2023
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