-1511

Appears in sequences

• Let phi = arccos(1/3), the dihedral angle of the regular tetrahedron. Then cos(n*phi) = a(n)/3^n.at n=7A025172
• Numerators of column 3 of table described in A051714/A051715.at n=14A051720
• a(n) = bin_prime_sum(fibonacci(A001651[n])), where fibonacci(A001651[n]) is A014437[n].at n=70A059878
• Expansion of 1/(1+x+2*x^3).at n=15A077974
• Main diagonal of triangle A097094; g.f. A(x) satisfies A(x)/(1-x-x^2) = A(x^2)^2/(1-x-x^3)^2.at n=19A097095
• Diagonal sums of triangle A110324.at n=54A110326
• G.f.: 1/(1 - x^3 - 2 x^4 + x^5).at n=34A122517
• Regular triangle, T(n, k) = f(n, k) - f(n, 0) + 1, where f(n, k) = Sum_{j=0..k} StirlingS1(n, n-j)*binomial(n,j) + Sum_{j=0..n-k} StirlingS1(n, n-j)*binomial(n, j), read by rows.at n=30A176155
• Regular triangle, T(n, k) = f(n, k) - f(n, 0) + 1, where f(n, k) = Sum_{j=0..k} StirlingS1(n, n-j)*binomial(n,j) + Sum_{j=0..n-k} StirlingS1(n, n-j)*binomial(n, j), read by rows.at n=33A176155
• Prime-generating polynomial: a(n) = 4*n^2 + 12*n - 1583.at n=3A182409
• Second differences of A000463; first differences of A188652.at n=54A188653
• Values of the prime-generating polynomial 4*n^2 - 284*n + 3449.at n=31A210626
• Values of the prime-generating polynomial 4*n^2 - 284*n + 3449.at n=40A210626
• Numerators of the inverse binomial transform of Bernoulli(n+2).at n=14A256671
• a(n) = 137*n^2 - 4043*n + 27277.at n=12A267706
• First differences of number of active (ON, black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 369", based on the 5-celled von Neumann neighborhood.at n=23A270793
• Expansion of e.g.f. exp(Sum_{k>=1} x^(k^2)*(1 - x^(k^2))/k^2).at n=7A308397
• Triangle read by rows: T(n,k) = Sum_{i=0..n-1} binomial(n-1, i)*T(n-1-i,k-1) - Sum_{i=1..n-1} binomial(n-1,i)*T(n-1-i,k) for 1 <= k <= n+1 with T(0,1) = 1 (and T(n,k) = 0 otherwise).at n=48A341287
• G.f. satisfies A(x) = A(x^3)/(A(x^2) - A(x^3)), with A(0) = 0, A'(0) = 1.at n=55A382317