-303

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=40A002121
• a(n) = floor(Sum_{k=0..n} tan(k)).at n=37A051508
• Expansion of (1-x)^(-1)/(1+x+x^2-x^3).at n=24A077908
• First order recursion: a(0)=1; a(n) = sigma(1,n) - a(n-1).at n=41A083238
• Expansion of g.f. (2*x^3 + 5) / ( -x^5 + x^3 + 1).at n=36A136598
• A transform of the Catalan numbers with a simple Hankel transform.at n=18A157127
• Imbalance of the number of partitions of n.at n=25A194795
• Array: row n shows the coefficients of the characteristic polynomial of the n-th principal submatrix of the symmetric matrix A202874; by antidiagonals.at n=17A202875
• Array: row n shows the coefficients of the characteristic polynomial of the n-th principal submatrix of f(i,j)=max(ceiling(i/j),ceiling(j/i)) (as in A204143).at n=41A204144
• a(n) = -3*a(n-1) + a(n-3), with a(0)=0, a(1)=-3, a(2)=12.at n=5A215919
• G.f.: x^((k^2 + k)/2) / (Product_{i=1..k} (1 - x^i) * Product_{r>=1} (1 + x^r)) with k = 2.at n=52A246581
• First differences of number of active (ON, black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 433", based on the 5-celled von Neumann neighborhood.at n=13A272148
• First differences of number of active (ON, black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 437", based on the 5-celled von Neumann neighborhood.at n=9A272156
• a(n) = -A292140(n)/2.at n=34A292141
• Expansion of Product_{k>=1} 1/(1 + x^k)^p(k), where p(k) = number of partitions of k (A000041).at n=18A304784
• Möbius transform of A332223.at n=51A332463
• Dirichlet convolution of A064413 (EKG-permutation) with the Dirichlet inverse of its inverse permutation.at n=44A349613
• Expansion of Sum_{k>0} (1/(1+x^k)^3 - 1).at n=22A363630
• a(n)=a(n-1) + prime(n) for n prime, and a(n)=-a(n-1) otherwise, with a(0)=0, with duplicates removed afterwards.at n=52A378677
• Shifts left one place under the inverse modulo 2 binomial transform.at n=55A380652