-249

Appears in sequences

• a(0) = 1, a(1) = 0, a(2) = -1; for n >= 3, a(n) = - a(n-2) + Sum_{ primes p with 3 <= p <= n} a(n-p).at n=37A002121
• Site percolation series for directed cubic lattice.at n=9A006837
• Unique attractor for (RIGHT then MOBIUS) transform.at n=55A007554
• sech(arcsin(arctan(x)))=1-1/2!*x^2+9/4!*x^4-249/6!*x^6+13297/8!*x^8...at n=3A012098
• sech(arctan(arcsin(x)))=1-1/2!*x^2+9/4!*x^4-249/6!*x^6+11953/8!*x^8...at n=3A012202
• 5th differences of partition numbers A000041.at n=38A081095
• First differences of roots of consecutive prime powers; a(1)=1.at n=69A088233
• Inverse binomial transform of number-theoretic triangle A109974.at n=50A109978
• G.f.: (x - 1)/(x^5 - x^3 - x^2 - x - 1).at n=47A115412
• a(n) = A118443(n)/(n+1), where A118443 is the row sums of triangle A118441.at n=7A118444
• Numerator of imaginary part of (3*i - 1)^(-n).at n=7A124871
• a(n) = -a(n-1) + 2a(n-2) - a(n-3), with a(0) = 0, a(1) = 1, a(2) = -3.at n=8A135019
• Riordan array ((1+x^2)/(1-x)^2, -x/(1-x)^2).at n=46A136672
• a(n) = 2*a(n-1) - 5*a(n-2), with a(1) = -1, a(2) = -7.at n=6A138749
• a(n) = Sum_{i=0..n-1} K(i,n)*i, where K(,) is Kronecker symbol.at n=82A228131
• a(n) = (3 - 6*n)*(-1)^n.at n=42A228935
• Expansion of f(-x^2)^2 * f(-x, x^2) / f(x^3)^3 in powers of x where f(,) is Ramanujan's general theta function.at n=33A254525
• Difference between sums of quadratic residues and non-residues modulo n that are coprime to n.at n=82A255643
• Difference between sums of quadratic residues and non-residues modulo n (residues are not necessarily coprime to n).at n=82A255644
• First differences of 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=35A272251