Donal LYONS - cp's OEIS frontend

User: Donal LYONS

Donal LYONS has authored 2 sequences.

A309777 Number of ways of being dealt an n-point Bridge hand.

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

Offset: 0

Donal LYONS, Aug 17 2019

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.

Cf. A363058.

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

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

A001368 Number of letters in n (in Irish Gaelic).

Original entry on oeis.org

4, 3, 2, 3, 7, 4, 2, 5, 3, 4, 4, 7, 6, 7, 11, 8, 6, 9, 7, 8, 4, 7, 6, 7, 11, 8, 6, 9, 7, 8, 6, 9, 8, 9, 13, 10, 8, 11, 9, 10, 8, 11, 10, 11, 15, 12, 10, 13, 11, 12, 5, 8, 7, 8, 12, 9, 7, 10, 8, 9, 6, 9, 8, 9, 13, 10, 8, 11, 9, 10, 6, 9, 8, 9, 13

Offset: 0

Donal LYONS

Lenition letters (lowercase h) are omitted in the count, thus "hocht" for 8 is considered to be "oct" with a letter count 3. Likewise, the particle "a" usually added to spoken numbers is omitted in the count, thus "fiche a do" for 22 is considered to be "fice do" with a letter count 6. - Sean A. Irvine, Jun 27 2012

Sean A. Irvine, Irish Gaelic numbers (without diacritical marks)
Donal LYONS, Considerations Re Counting
Index entries for sequences related to number of letters in n

Extended and corrected by Sean A. Irvine, Jun 27 2012

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User: Donal LYONS

A309777 Number of ways of being dealt an n-point Bridge hand.

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A001368 Number of letters in n (in Irish Gaelic).

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