A086401 a(n) = M(n) (mod n) where M(n) = A001006(n) is the n-th Motzkin number.
0, 0, 1, 1, 1, 3, 1, 3, 7, 8, 1, 7, 1, 10, 12, 11, 1, 6, 1, 19, 0, 3, 1, 21, 1, 16, 7, 5, 1, 1, 1, 19, 18, 20, 23, 7, 1, 3, 7, 17, 1, 36, 1, 41, 9, 26, 1, 21, 1, 28, 24, 45, 1, 33, 18, 43, 45, 32, 1, 39, 1, 34, 24, 51, 51, 42, 1, 19, 30, 7, 1, 9, 1, 40, 57, 57, 19, 24, 1, 17, 61, 44, 1, 37, 51
Offset: 1
Keywords
Links
- Amiram Eldar, Table of n, a(n) for n = 1..10000
Programs
-
Mathematica
motz[0] = motz[1] = 1; motz[n_] := motz[n] = ((2*n + 1)*motz[n-1] + 3*(n-1)*motz[n-2])/(n+2); a[n_] := Mod[motz[n], n]; Array[a, 100] (* Amiram Eldar, Apr 20 2025 *)
Formula
a(n) = 0 if and only if n is in A266969. - Amiram Eldar, Apr 20 2025
Extensions
Data corrected by Amiram Eldar, Apr 20 2025
Comments