login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A309777 Number of ways of being dealt an n-point Bridge hand. 0
1, 4, 10, 24, 51, 96, 170, 284, 445, 664, 952, 1304, 1716, 2184, 2680, 3176, 3650, 4064, 4380, 4584, 4658, 4584, 4380, 4064, 3650, 3176, 2680, 2184, 1716, 1304, 952, 664, 439, 268, 148, 64, 25, 4 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Points are counted in the standard (Milton Work) way, Ace=4, King=3, Queen=2, Jack=1, all other cards = 0. The first term a(0) then is the number of ways of being dealt a "Yarborough" (a hand with 0 points). That consists of 13 cards with 0 Aces, 0 Kings, 0 Queens and 0 Jacks which, all other cards being considered as indistinguishable, can be dealt in 1 way. The final term, a(37), represents a 37-point hand consisting of 4 Aces, 4 Kings, 4 Queens and 1 Jack. This can be dealt in 4 ways (the Jack is of any one of the four suits Clubs, Diamonds, Hearts, Spades). May you be dealt many of them (but not against me). The sequence would of course be symmetric, and sum to 2^16 except for the restriction to 13 cards.

LINKS

Table of n, a(n) for n=0..37.

FORMULA

a(n) = [y^n][x^13]((Product_{k=1..4} 1 + x*y^k)^4/(1-x)). - Andrew Howroyd, Aug 23 2019

PROG

(PARI) Vecrev(polcoef(prod(k=1, 4, (1 + x*y^k + O(x*x^13))^4)/(1-x), 13)) \\ Andrew Howroyd, Aug 22 2019

CROSSREFS

Sequence in context: A001979 A209970 A211392 * A128516 A022569 A093831

Adjacent sequences:  A309774 A309775 A309776 * A309778 A309779 A309780

KEYWORD

nonn,fini,full

AUTHOR

Donal LYONS, Aug 17 2019

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified June 17 00:17 EDT 2021. Contains 345080 sequences. (Running on oeis4.)