30537

Appears in sequences

• Riordan numbers: a(n) = (n-1)*(2*a(n-1) + 3*a(n-2))/(n+1).at n=14A005043
• Number of partitions satisfying cn(0,5) + cn(1,5) + cn(4,5) <= cn(2,5) + cn(3,5).at n=44A039878
• a(n) = a(n-1) + 2*a(floor(n/2)) if n > 0, otherwise 1.at n=34A058039
• Bisection of Motzkin sums (A005043).at n=7A099251
• Expansion of (sqrt(1+3*x) + sqrt(1-x))/(2*sqrt(1-x)).at n=15A099323
• Triangle read by rows: T(n,k) is the number of paths in the first quadrant from (0,0) to (n,0), consisting of steps U=(1,1), D=(1,-1), h=(1,0) and H=(2,0), having k doublerises (i.e., UU's) (0 <= k <= floor(n/2) - 1 for n >= 2).at n=32A132279
• Number of Dyck paths of semilength n, having no ascents and no descents of length 1, and having no peaks at odd level.at n=20A167635
• Row sums of the triangle in A199333.at n=14A199694
• Number of all possible tetrahedra of any size and orientation, formed when intersecting the original regular tetrahedron by planes parallel to its sides and dividing its edges into n equal parts.at n=25A216173
• Array T(n,k) of the expected value of trace(O)^(2k), where O is an n X n orthogonal matrix randomly selected according to Haar measure, read by antidiagonals.at n=42A247306
• Numbers k such that 2*k+1 and 10*k+1 are both triangular numbers (A000217).at n=1A279042
• a(n) = [x^n] (1 - 2*x - sqrt((1 - 3*x)/(1 + x)))/(2*x^3).at n=12A342912
• Array read by ascending antidiagonals: A(n, s) is the n-th s-Catalan number.at n=29A349934
• G.f. A(x) satisfies: A(x) = 1 + x^2 * A(x/(1 - 2*x)) / (1 - 2*x).at n=10A351143
• a(n) is the maximum integer for which some minimum-length sum equaling a(n) of perfect squares less than n^2 excludes (n-1)^2.at n=31A377084
• Two-Catalan Triangle read by rows, for n>=0 and k>=0.at n=49A380912
• Numerators of rational coefficients which are ratio of Brent's coefficients -A[n,2]/A343480.at n=30A380947