OFFSET
1,1
REFERENCES
D. M. Bressoud, Proofs and Confirmations, Camb. Univ. Press, 1999; triangle on page 6, numerators.
LINKS
Michael De Vlieger, Table of n, a(n) for n = 1..11325 (rows 1 <= n <= 150)
Eric Weisstein's World of Mathematics, Alternating Sign Matrix.
D. Zeilberger, Dave Robbins's Art of Guessing, Adv. in Appl. Math. 34 (2005), 939-954.
FORMULA
From Thomas Baruchel, Jun 26 2018: (Start)
a(n,k) = (binomial(n+2,k+1) + binomial(n+1,k) + binomial(n,k) - binomial(n,k+1))/2.
a(n,k) = binomial(n-1,k-1) + binomial(n-1,k) + binomial(n,k-1) + binomial(n,k). (End)
EXAMPLE
Triangle begins:
2;
2, 3;
2, 5, 4;
2, 7, 9, 5;
2, 9, 16, 14, 6;
2, 11, 25, 30, 20, 7;
...
MATHEMATICA
Table[(Binomial[n + 2, k + 1] + Binomial[n + 1, k] + Binomial[n, k] - Binomial[n, k + 1])/2, {n, 0, 11}, {k, 0, n}] // Flatten (* Michael De Vlieger, Jun 29 2018 *)
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
EXTENSIONS
More terms from James A. Sellers
STATUS
approved