14536

Properties

Appears in sequences

• a(n) = C(n,5) + C(n,4) - C(n,3) + 1, n >= 7.at n=13A005288
• Numbers k such that the period of the continued fraction for sqrt(k) contains exactly 19 ones.at n=9A031787
• Number of permutations P of {1,2,...,n} such that P(1)=1 and |P^-1(i+1)-P^-1(i)| equals 1 or 2 for i=1,2,...,n-1.at n=24A038718
• At stage 1, start with a unit equilateral equiangular triangle. At each successive stage add 3*(n-1) new triangles around outside with edge-to-edge contacts. Sequence gives number of triangles (regardless of size) at n-th stage.at n=31A064412
• The 5-cycle of the n => sigma(n)-n process, where sigma(n) is the sum of divisors of n (A000203).at n=3A072891
• Numbers k such that k^4 + 1, (k+2)^4 + 1 and (k+4)^4 + 1 are all primes.at n=16A073476
• Conjectured list of sociable numbers.at n=4A122726
• Number of reduced words of length n in the Weyl group A_16.at n=5A161477
• Those positive integers n where, when written in binary, there are exactly k number of runs (of either 0's or 1's) each of exactly k length, for all k where 1<=k<=m, for some positive integer m.at n=39A175356
• Conjectured list of multisociable numbers.at n=22A183019
• Number of lower triangles of an n X n 0..7 array with each element differing from all of its diagonal, vertical, antidiagonal and horizontal neighbors by one or less.at n=3A195231
• Number of lower triangles of a 4 X 4 0..n array with each element differing from all of its diagonal, vertical, antidiagonal and horizontal neighbors by one or less.at n=6A195234
• Number of n X n arrays of the minimum value of corresponding elements and their horizontal, diagonal or antidiagonal neighbors in a random, but sorted with lexicographically nondecreasing rows and nonincreasing columns, 0..2 n X n array.at n=4A219877
• Number of nX5 arrays of the minimum value of corresponding elements and their horizontal, diagonal or antidiagonal neighbors in a random, but sorted with lexicographically nondecreasing rows and nonincreasing columns, 0..2 nX5 array.at n=4A219880
• T(n,k)=Number of nXk arrays of the minimum value of corresponding elements and their horizontal, diagonal or antidiagonal neighbors in a random, but sorted with lexicographically nondecreasing rows and nonincreasing columns, 0..2 nXk array.at n=40A219883
• Number of 5Xn arrays of the minimum value of corresponding elements and their horizontal, diagonal or antidiagonal neighbors in a random, but sorted with lexicographically nondecreasing rows and nonincreasing columns, 0..2 5Xn array.at n=4A219886
• a(n) is the number of terms in the expansion of (x-y)*(x^4-y^4)*(x^9-y^9)*...*(x^(n^2)-y^(n^2)).at n=34A225549
• Positions of the integers in the ordering of rational numbers as generated by the rules: 1 is in S, and if nonzero x is in S, then x+1 and -1/x are in S. (See Comments.)at n=31A226137
• G.f.: Sum_{n>=0} x^n / (1-x)^(2*n+1) * [ Sum_{k=0..n} C(n,k)^2*x^k ]^2.at n=7A227845
• Number of n X 7 0..2 arrays with horizontal differences mod 3 never 1, vertical differences mod 3 never -1, and rows and columns lexicographically nondecreasing.at n=5A229444