2031616

Appears in sequences

• Expansion of cos x (1 + sin x ) /cos 2x.at n=9A000825
• E.g.f. cos(x)/(cos(x) - sin(x)).at n=9A000828
• Binomial transform, alternating in sign, of Lucas generalized numbers S(n): S(n) = S(n-1) + S(n-2) + S(n-3), S(0)=3, S(1)=1, S(2)=3.at n=32A073314
• Denominators in the Maclaurin series for arctan(1+x).at n=30A075554
• 4th binomial transform of (1,3,0,0,0,0,0,.....).at n=9A081039
• Third binomial transform of C(n+2,2).at n=9A081893
• a(n) = 2^n*(n^2 - n + 8)/8.at n=16A081908
• Number of n X n matrices over GF(2) with characteristic polynomial x^(n-1) * (x-1).at n=4A088668
• Expansion of g.f. (1 - x)^2*(1 + x) / (1 - 2*x)^2.at n=18A106472
• Let S(n)=Sigma(n)/2. Numbers n such that S(S(n))=n, 1/2-Sociable number of order 1 or 2.at n=33A113791
• a(n) = (2*n + 1) * 2^(n + 1).at n=15A118417
• a(n) = n-th integer from among those positive integers with an exponent of n in their prime-factorizations.at n=15A123904
• a(n) = n*2^floor((n+1)/2).at n=31A132314
• a(0)=7, a(n) = 2*a(n-1) + 2^(n-1) for n > 0.at n=17A159695
• a(n) = Sum_{d|n} Möbius(n/d)*d^5/phi(n).at n=31A160893
• Numbers with 34 divisors.at n=9A175744
• Conjectured list of smallest members of fully k-sociable cycles of order r.at n=32A183026
• a(n) = (n/4)*2^(n/2)*((1+sqrt(2))^2 + (-1)^n*(1-sqrt(2))^2).at n=31A187272
• Monotonic ordering of nonnegative differences 8^i-4^j, for 40>= i>=0, j>=0.at n=36A192168
• Number of 0..n arrays x(0..4) of 5 elements with each no smaller than the sum of its previous elements modulo (n+1).at n=29A200254