A275481 Integers that appear uniquely in the Catalan triangle, A009766.
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
Links
- 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, and 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
Crossrefs
Programs
-
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 *) -
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))
Comments