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Search: id:A048601
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| A048601 |
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Robbins triangle read by rows: T(n,k) = number of alternating sign n X n matrices with a 1 at top of column k (n >= 1, 1<=k<=n) |
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+0
8
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| 1, 1, 1, 2, 3, 2, 7, 14, 14, 7, 42, 105, 135, 105, 42, 429, 1287, 2002, 2002, 1287, 429, 7436, 26026, 47320, 56784, 47320, 26026, 7436, 218348, 873392, 1813968, 2519400, 2519400, 1813968, 873392, 218348, 10850216, 48825972, 113927268, 179028564
(list; table; graph; listen)
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OFFSET
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1,4
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COMMENT
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An alternating sign matrix is a matrix of 0's and 1's such that (a) the sum of each row and column is 1; (b) the nonzero entries in each row and column alternate in sign.
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REFERENCES
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D. Bressoud, Proofs and Confirmations: The Story of the Alternating Sign Matrix Conjecture, Cambridge University Press, 1999, p. 5.
D. Bressoud and J. Propp, How the alternating sign matrix conjecture was solved, Notices Amer. Math. Soc., 46 (No. 6, 1999), 637-646.
D. Zeilberger, Dave Robbins's Art of Guessing, Adv. in Appl. Math. 34 (2005), 939-954.
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LINKS
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N. J. A. Sloane, Table of n, a(n) for n = 1..1275 [Rows 1..50, flattened]
P. Di Francesco, A refined Razumov-Stroganov conjecture II
Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics.
D. Zeilberger, [math/9606224] Proof of the Refined Alternating Sign Matrix Conjecture
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FORMULA
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T(n, k)=binomial(n+k-2, k-1)*((2*n-k-1)!/(n-k)!)*product(((3*j+1)!/(n+j)!), j=0..n-2);
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EXAMPLE
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Triangle begins:
1,
1,1,
2,3,2,
7,14,14,7,
42,105,135,105,42,
429,1287,2002,2002,1287,429,
7436,26026,47320,56784,47320,26026,7436,
...
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MAPLE
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T:=(n, k)-> binomial(n+k-2, k-1)*((2*n-k-1)!/(n-k)!)*product(((3*j+1)!/(n+j)!), j=0..n-2);
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CROSSREFS
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Row sums (also borders) of triangle give A005130. Cf. A051106.
Sequence in context: A129022 A122076 A014784 this_sequence A008317 A139011 A152297
Adjacent sequences: A048598 A048599 A048600 this_sequence A048602 A048603 A048604
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KEYWORD
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nonn,tabl,nice,easy
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
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More terms from James A. Sellers (sellersj(AT)math.psu.edu)
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