21320

Appears in sequences

• Number of "cubic partitions" of n: expansion of Product_{k>0} 1/((1-x^(2k))^2*(1-x^(2k-1))) in powers of x.at n=27A002513
• a(n) = 2*binomial(n,3).at n=41A007290
• Expansion of e.g.f.: tan(sin(x)*log(x+1)).at n=8A012282
• Expansion of e.g.f. arctanh(sin(x)*log(x+1))=2/2!*x^2-3/3!*x^3+4/4!*x^4-20/5!*x^5...at n=8A012287
• Numbers k such that the continued fraction for sqrt(k) has even period and if the last term of the periodic part is deleted the central term is 73.at n=26A031571
• Numbers k such that the least term in the periodic part of the continued fraction for sqrt(k) is 73.at n=1A031751
• Base-4 numbers whose list of divisors (in base 4) contains each digit 0-3 the same number of times.at n=2A045813
• a(1) = 1, a(2) = 2, a(3) = 3, a(n+3) = a(n) + a(n+1).at n=34A084338
• Diagonal sums of Riordan array (1-x-x^2,x(1-x)).at n=38A109266
• Number of permutations of length n which avoid the patterns 1234, 2341, 3421.at n=10A116818
• a(n) = Sum_{k=1..phi(n)-1} t(n,k)*t(n,k+1), where t(n,k) is the k-th positive integer which is coprime to n and phi(n) is the number of positive integers which are <= n and are coprime to n.at n=40A119584
• A triangular array distributing the values of sequence A072213 (cf. A115994).at n=37A128626
• a(n) = 13*n*(n+1).at n=40A173307
• Sums of two successive primes s such that s+-3 are primes.at n=37A179485
• Sum of the numbers already removed (including the target number) in the first jump of a Sieve of Eratosthenes table.at n=31A179654
• Degrees of irreducible representations of orthogonal group O8-(3).at n=21A214474
• Primitive integer length of the side of an origin-centered square that contains inside its boundary a point with integer coordinates that is an integer distance from three of the four corners.at n=16A215365
• Size of the smallest conjugacy class of size greater than 1 of the alternating group of degree n.at n=37A237036
• Number of (n+2) X (5+2) 0..1 arrays with no 3 x 3 subblock diagonal sum less than the antidiagonal sum or central row sum less than the central column sum.at n=6A258891
• Number of (n+2) X (7+2) 0..1 arrays with no 3 X 3 subblock diagonal sum less than the antidiagonal sum or central row sum less than the central column sum.at n=4A258893