

A309777


Number of ways of being dealt an npoint 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
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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 37point 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/(1x)).  Andrew Howroyd, Aug 23 2019


PROG

(PARI) Vecrev(polcoef(prod(k=1, 4, (1 + x*y^k + O(x*x^13))^4)/(1x), 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



