30372

Appears in sequences

• Generalized Catalan numbers: a(n+1) = a(n) + Sum_{k=1..n-1} a(k)*a(n-1-k).at n=15A004148
• Essentially same as A004148.at n=16A025241
• Decimal part of cube root of a(n) starts with 2: first term of runs.at n=30A034128
• Number of A095748-primes in range ]2^n,2^(n+1)].at n=29A095758
• Triangle read by rows: T(n,k) is the number of Motzkin paths of length n with k valleys (n>=0, 0<=k<=floor(n/2)-1; a valley is a downstep followed by an upstep).at n=44A097885
• Triangle read by rows: T(n,k) is the number of peakless Motzkin paths in which the k-th step is the leftmost (1,0)-step (can be easily expressed using RNA secondary structure terminology).at n=64A098086
• Maximal troughs in decimal expansions of Pi: positions of troughs equal to 8.at n=32A105276
• Number of base 20 circular n-digit numbers with adjacent digits differing by 7 or less.at n=4A125432
• Triangle read by rows: T(n,k) is the number of weighted lattice paths in L_n having k (1,-1)-returns to the horizontal axis. The members of L_n are paths of weight n that start at (0,0), end on the horizontal axis and whose steps are of the following four kinds: an (1,0)-step with weight 1, an (1,0)-step with weight 2, a (1,1)-step with weight 2, and a (1,-1)-step with weight 1. The weight of a path is the sum of the weights of its steps.at n=40A182896
• Number of elevated peakless Motzkin paths.at n=17A203019
• Number of 0..n arrays of length 5 with each element differing from at least one neighbor by something other than 1, starting with 0.at n=12A221543
• Partial sums of the number of active (ON, black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 446", based on the 5-celled von Neumann neighborhood.at n=39A272250
• Length of shortest prefix of the Kolakoski sequence K (A000002) containing all blocks of length n that appear in K.at n=48A283511
• Expansion of (1 - x - x^2 - sqrt((1 - x - x^2)^2 - 4*x^3))/(2*x^3) in powers of x.at n=14A292460
• Number of separable partitions of n in which the number of distinct (repeatable) parts is 5.at n=45A325649
• a(n) is the cardinality of S(n), the subset of partitions of n such that there are enough smaller parts to add together to be greater than a larger part.at n=38A338085
• Numbers that are the sum of seven fourth powers in eight or more ways.at n=9A345574
• Numbers that are the sum of seven fourth powers in exactly eight ways.at n=5A345830
• Irregular table read by rows: T(n,k) is the number of k-gons, k>=3, among all distinct circles that can be constructed from the 4 vertices and the equally spaced 4*n points placed on the sides of a square, using only a compass.at n=36A372980