103049

Properties

Appears in sequences

• Schroeder's second problem (generalized parentheses); also called super-Catalan numbers or little Schroeder numbers.at n=9A001003
• Erroneous version of A001003.at n=9A010682
• Triangle of numbers S(x,y) = number of lattice paths from (0,0) to (x,y) that use step set { (0,1), (1,0), (2,0), (3,0), ....} and never pass below y = x.at n=54A011117
• Least prime in A031936 (lesser of 18-twins) whose distance to the next 18-twin is 2*n.at n=28A052358
• Smaller of two consecutive primes whose sum is a square.at n=28A061275
• Lesser of consecutive primes whose sum is a perfect power (A001597).at n=34A091624
• Primes in A001003.at n=3A092840
• Triangle read by rows: T(n,k) is number of Schroeder paths of length 2n and having k peaks at height 1, for 0 <= k <= n.at n=45A104219
• Triangle read by rows: T(n,k) is the number of Delannoy paths of length n, having k EE's and NN's crossing the line y = x (i.e., two consecutive E steps from the line y = x+1 to the line y = x-1 or two consecutive N steps from the line y = x-1 to the line y = x+1).at n=29A110123
• Triangular array formed by the little Schröder numbers s(n,k).at n=36A110440
• Triangle read by rows: T(n,k) is the number of bicolored Dyck paths of semilength n and having k peaks of the form ud (0 <= k <= n). A bicolored Dyck path is a Dyck path in which each up-step is of two kinds: u and U.at n=45A114608
• Triangle read by rows: T(n,k) is the number of paths of length n in the first quadrant, starting at the origin, ending at height k and consisting of 2 kind of upsteps U=(1,1) (U1 and U2), 3 kind of flatsteps F=(1,0) (F1, F2 and F3) and 1 kind of downsteps D=(1,-1).at n=36A134426
• Primes of the form n^2+8.at n=25A138338
• Eigentriangle, row sums = A006318.at n=45A144156
• Super-Catalan triangle (read by rows) = triangular array associated with little Schroeder numbers (read by rows): T(0,0)=1, T(p,q) = T(p,q-1) if 0 < p = q, T(p,q) = T(p,q-1) + T(p-1,q) + T(p-1,q-1) if -1 < p < q and T(p,q) = 0 otherwise.at n=53A144944
• Super-Catalan triangle (read by rows) = triangular array associated with little Schroeder numbers (read by rows): T(0,0)=1, T(p,q) = T(p,q-1) if 0 < p = q, T(p,q) = T(p,q-1) + T(p-1,q) + T(p-1,q-1) if -1 < p < q and T(p,q) = 0 otherwise.at n=54A144944
• Numbers n such that 17, n, n+1 are the sides of a Heron triangle, i.e., a triangle with integer sides and integer area.at n=17A145820
• Prime numbers p such that 17,p,p+1 is a Heron triangle, that is a triangle with integer sides and integer area.at n=2A145821
• The number of even separable permutations of length n.at n=9A165328
• The Riordan square of the little Schröder numbers A001003.at n=45A172094