A275481 n appears once in c_{m,k} for integers m >= k >= 1 where c_{m,k} = ((n+k)!(n-k+1))/((k)!(n+1)!).

3, 4, 6, 7, 8, 10, 11, 12, 13, 15, 16, 17, 18, 19, 21, 22, 23, 24, 25, 26, 29, 30, 31, 32, 33, 34, 36, 37, 38, 39, 40, 41, 43, 45, 46, 47, 49, 50, 51, 52, 53, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 66, 67, 68, 69, 70, 71, 72, 73, 74, 76, 78, 79, 80, 81, 82, 83, 84, 85

Offset

1,1

Comments

Integers that appear uniquely in the Catalan triangle, A009766.

Links

Table of n, a(n) for n=1..69.

D. F. Bailey, Counting arrangements of 1's and-1's, Mathematics Magazine, 69 (1996): 128-131.

Nathaniel Benjamin, Grant Fickes, Eugene Fiorini, Edgar Jaramillo Rodriguez, Eric Jovinelly, Tony W. H. Wong, Primes and Perfect Powers in the Catalan Triangle, J. Int. Seq., Vol. 22 (2019), Article 19.7.6.

Eric W. Weisstein, Catalan's Triangle

Mathematica

Block[{T, nn = 85}, T[n_, k_] := T[n, k] = Which[k == 0, 1, k > n, 0, True, T[n - 1, k] + T[n, k - 1]]; Rest@ Complement[Range@ nn, Union@ Flatten@ Table[T[n, k], {n, 2, nn}, {k, 2, n}]]] (* Michael De Vlieger, Feb 04 2020, after Jean-François Alcover at A009766 *)

Prog

(Python)
#prints the unique integers less than k
def Unique_Catalan_Triangle(k):
    t = []
    t.append([])
    t[0].append(1)
    for h in range(1, k):
        t.append([])
        t[0].append(1)
    for i in range(1, k):
        for j in range(0, k):
            if i>j:
                t[i].append(0)
            else:
                t[i].append(t[i-1][j] + t[i][j-1])
    l = []
    for r in range(0, k):
        for s in range(0, k):
            l.append(t[r][s])
    unique = []
    for n in l:
        if n <= k and l.count(n) == 1 :
            unique.append(n)
    print sorted(unique)

Crossrefs

Subsequence of A007401, which is the complement of A000096.

Cf. A009766, A275586 (complement).

Sequence in context: A075747 A143344 A007401 * A234349 A042954 A361457

Adjacent sequences: A275478 A275479 A275480 * A275482 A275483 A275484

Keyword

easy,nonn

Author

Edgar Jaramillo Rodriguez, Nathaniel Benjamin, Eric Jovinelly, Eugene Fiorini, Jul 29 2016

Status

approved