Sequences

n-th nonnegative integer k satisfying cos(k) > cos(k+1).

n-th nonnegative integer k satisfying cos(k) > sin(k+1).

Numbers k such that |sin(k)*sin(k+2)| < (sin(k+1))^2.

a(n) = n-th nonnegative integer k satisfying |cos(k)*cos(k+2)| > (cos(k+1))^2.

|sin(n)| < |sin(n+1)|.

Numbers k such that |sin(k)| > |cos(k+1)|.

Nonnegative integers k such that |cos(k)| > |sin(k+1)|.

a(n) = n-th nonnegative integer k satisfying sin(k) < cos(k) < sin(k+1).

a(n) is the n-th nonnegative integer k satisfying |sin(k)| < |cos(k)| < |sin(k+1)|.

sin(n) > cos(n) > sin(n+1).

n-th nonnegative integer k satisfying |sin(k)| > |cos(k)| > |sin(k+1)|.

|sin(2n)| > |sin(n)|.

Irregular triangular array T read by rows: T(0,0) = 1, T(0,1) = T(0,2) = 0; T(1,0) = T(1,1) = T(1,2) = 1, T(1,3) = 0; for n >= 2, T(n,0) = 1, T(n,1) = T(n-1,0) + T(n-1,1), T(n,k) = T(n-1,k-2) + T(n-1,k-1) + T(n-1,k) for k = 2,3,...,n+1 and T(n,n+2) = T(n-1,n) + T(n-1,n+1).

Expansion of 1/((1-2*x)*(1-6*x)*(1-7*x)*(1-8*x)).

Number of paths in the plane x >= 0 and y >= -2, from (0,0) to (n,0), and consisting of steps U = (1,1), D = (1,-1) and H = (1,0).

Expansion of 1/((1-2*x)*(1-6*x)*(1-7*x)*(1-9*x)).

a(n) = number of (s(0), s(1), ..., s(n)) such that s(i) is a nonnegative integer and |s(i) - s(i-1)| <= 1 for i = 1,2,...,n, s(0) = 2, s(n) = 4. Also a(n) = T(n,n-2), where T is the array in A026323.

a(n) = number of (s(0), s(1), ..., s(n)) such that s(i) is a nonnegative integer and |s(i) - s(i-1)| <= 1 for i = 1,2,...,n, s(0) = 2, s(n) = 5. Also a(n) = T(n,n-3), where T is the array in A026323.

a(n) = number of (s(0), s(1), ..., s(n)) such that s(i) is a nonnegative integer and |s(i) - s(i-1)| <= 1 for i = 1,2,...,n, s(0) = 2, s(n) = 6. Also a(n) = T(n,n-4), where T is the array in A026323.

a(n) = number of (s(0), s(1), ..., s(n)) such that s(i) is a nonnegative integer and |s(i) - s(i-1)| <= 1 for i = 1,2,...,n, s(0) = 2, s(2n) = n+1. Also a(n) = T(2n,n+1), where T is the array in A026323.

a(n) = T(2n-1,n), where T is the array in A026323.

a(n) = T(2n,n), where T is the array in A026323.

a(n) = T(3n,n), where T is the array in A026323.

T(4n,n), where T is the array in A026323.

a(n) = T(2n,n-1), where T is the array in A026323.

a(n) = T(n,[ n/2 ]), where T is the array in A026323.

a(n) = 4^n*(4^n - 1)/2.

a(n) = a(m) if a(m) has already occurred exactly once and n = m+[ m/2 ]+1, else a(n) = least positive integer that has not yet occurred.

a(n) = least k such that s(k) = n, where s = A026338.

a(n) = greatest k such that s(k) = n, where s = A026338.

a(n) = sum of the numbers between the two n's in A026338.

a(n) = a(m) if a(m) has already occurred exactly once and n = m+[ (m+1)/2 ], else a(n) = least positive integer that has not yet occurred.

Least k such that s(k) = n, where s = A026342.

a(n) = greatest k such that s(k) = n, where s = A026342.

a(n) = sum of the numbers between the two n's in A026342.

a(n) = a(m) if a(m) has already occurred exactly once and n = a(m)+[ 3m/2 ], else a(n) = least positive integer that has not yet occurred.

a(n) = least k such that s(k) = n, where s = A026346.

Greatest k such that s(k) = n, where s = A026346.

a(n) = sum of the numbers between the two n's in A026346.

a(n) = a(m) if a(m) has already occurred exactly once and n = a(m)+m-1, else a(n) = least positive integer that has not yet occurred.

a(n) = floor(n*phi) + 1, where phi = (1+sqrt(5))/2.

a(n) = floor(n*phi) + n + 1 where phi is the golden ratio A001622.

a(n) = sum of the numbers between the two n's in A026350.

a(n) = a(m) if a(m) has already occurred exactly once and n = a(m)+m-2, else a(n) = least positive integer that has not yet occurred.

a(n) = least k such that s(k) = n+1, where s = A026354.

a(n) = floor((n-1)*phi) + n + 1, n > 0, where phi = (1+sqrt(5))/2.

a(n) = sum of the numbers between the two n's in A026354.

a(n) = a(m) if a(m) has already occurred exactly once and n = a(m)+2m-2, else a(n) = least positive integer that has not yet occurred.

a(n) = least k such that s(k) = n, where s = A026358.

a(n) = greatest k such that s(k) = n, where s = A026358.