Sequences

392,541 sequences

a(n) = T(2n-1,n), where T is the array defined in A026105.A026111
a(n) = T(2n-1,n), where T is the array defined in A026105.
a(n) = T(2n,n), where T is the array defined in A026105.A026112
a(n) = T(2n,n), where T is the array defined in A026105.
T(3n,n), where T is the array defined in A026105.A026113
T(3n,n), where T is the array defined in A026105.
T(4n,n), where T is the array defined in A026105.A026114
T(4n,n), where T is the array defined in A026105.
a(n) = T(2n,n-1), where T is the array defined in A026105.A026115
a(n) = T(2n,n-1), where T is the array defined in A026105.
T(2n,n+1), where T is the array defined in A026105.A026116
T(2n,n+1), where T is the array defined in A026105.
T(n,[ n/2 ]), where T is the array defined in A026105.A026117
T(n,[ n/2 ]), where T is the array defined in A026105.
Number of polyhexes of class PF2 (with two catafusenes annealated to pyrene).A026118
Number of polyhexes of class PF2 (with two catafusenes annealated to pyrene).
Bisection of A000016 (also of A000013).A026119
Bisection of A000016 (also of A000013).
Triangle T by rows: second differences of Motzkin triangle (A026300), (i >= -1, -1<=j<=i).A026120
Triangle T by rows: second differences of Motzkin triangle (A026300), (i >= -1, -1<=j<=i).
a(n) = 3^n*(3^n-1)/2.A026121
a(n) = 3^n*(3^n-1)/2.
a(n) is the number of (s(0),s(1),...,s(n)) such that every s(i) is a nonnegative integer, s(0) = 1, s(n) = 1, |s(1) - s(0)| = 1, |s(i) - s(i-1)| <= 1 for i >= 2. Also a(n) = T(n,n), where T is the array in A026120.A026122
a(n) is the number of (s(0),s(1),...,s(n)) such that every s(i) is a nonnegative integer, s(0) = 1, s(n) = 1, |s(1) - s(0)| = 1, |s(i) - s(i-1)| <= 1 for i >= 2. Also a(n) = T(n,n), where T is the array in A026120.
a(n) = number of (s(0),s(1),...,s(n)) such that every s(i) is a nonnegative integer, s(0) = 1, s(n) = 2, |s(1) - s(0)| = 1, |s(i) - s(i-1)| <= 1 for i >= 2. Also a(n) = T(n,n-1), where T is the array in A026120; a(n) = U(n,n+1), where U is the array in A026148.A026123
a(n) = number of (s(0),s(1),...,s(n)) such that every s(i) is a nonnegative integer, s(0) = 1, s(n) = 2, |s(1) - s(0)| = 1, |s(i) - s(i-1)| <= 1 for i >= 2. Also a(n) = T(n,n-1), where T is the array in A026120; a(n) = U(n,n+1), where U is the array in A026148.
a(n) = number of (s(0),s(1),...,s(n)) such that every s(i) is a nonnegative integer, s(0) = 1, s(n) = 3, |s(1) - s(0)| = 1, |s(i) - s(i-1)| <= 1 for i >= 2. Also a(n) = T(n,n-2), where T is the array in A026120.A026124
a(n) = number of (s(0),s(1),...,s(n)) such that every s(i) is a nonnegative integer, s(0) = 1, s(n) = 3, |s(1) - s(0)| = 1, |s(i) - s(i-1)| <= 1 for i >= 2. Also a(n) = T(n,n-2), where T is the array in A026120.
a(n) = number of (s(0),s(1),...,s(n)) such that every s(i) is a nonnegative integer, s(0) = 1, s(n) = 4, |s(1) - s(0)| = 1, |s(i) - s(i-1)| <= 1 for i >= 2. Also a(n) = T(n,n-3), where T is the array in A026120.A026125
a(n) = number of (s(0),s(1),...,s(n)) such that every s(i) is a nonnegative integer, s(0) = 1, s(n) = 4, |s(1) - s(0)| = 1, |s(i) - s(i-1)| <= 1 for i >= 2. Also a(n) = T(n,n-3), where T is the array in A026120.
a(n) = number of (s(0),s(1),...,s(n)) such that every s(i) is a nonnegative integer, s(0) = 1, s(n) = 5, |s(1) - s(0)| = 1, |s(i) - s(i-1)| <= 1 for i >= 2. Also a(n) = T(n,n-4), where T is the array in A026120.A026126
a(n) = number of (s(0),s(1),...,s(n)) such that every s(i) is a nonnegative integer, s(0) = 1, s(n) = 5, |s(1) - s(0)| = 1, |s(i) - s(i-1)| <= 1 for i >= 2. Also a(n) = T(n,n-4), where T is the array in A026120.
a(n) = T(2n-1,n-1), where T is the array in A026120.A026127
a(n) = T(2n-1,n-1), where T is the array in A026120.
a(n) = T(2n,n), where T is the array in A026120.A026128
a(n) = T(2n,n), where T is the array in A026120.
a(n) = T(3n,n), where T is the array in A026120.A026129
a(n) = T(3n,n), where T is the array in A026120.
T(4n,n), where T is the array in A026120.A026130
T(4n,n), where T is the array in A026120.
a(n) = T(2n,n-2), where T is the array in A026120.A026131
a(n) = T(2n,n-2), where T is the array in A026120.
a(n) = A026120(2n,n+1).A026132
a(n) = A026120(2n,n+1).
a(n) = T(n,[ n/2 ] - 1), where T is the array in A026120.A026133
a(n) = T(n,[ n/2 ] - 1), where T is the array in A026120.
a(n) = Sum_{k=1..n} T(k, k-1), where T is the array in A026120.A026134
a(n) = Sum_{k=1..n} T(k, k-1), where T is the array in A026120.
Number of (s(0),s(1),...,s(n)) such that every s(i) is a nonnegative integer, s(0) = 1, |s(1) - s(0)| = 1, |s(i) - s(i-1)| <= 1 for i >= 2. Also sum of numbers in row n+1 of the array T defined in A026120.A026135
Number of (s(0),s(1),...,s(n)) such that every s(i) is a nonnegative integer, s(0) = 1, |s(1) - s(0)| = 1, |s(i) - s(i-1)| <= 1 for i >= 2. Also sum of numbers in row n+1 of the array T defined in A026120.
Lexicographically earliest permutation of the positive integers such that |a(n)-n| = [a(n)/2].A026136
Lexicographically earliest permutation of the positive integers such that |a(n)-n| = [a(n)/2].
a(n) = position of n in A026136.A026137
a(n) = position of n in A026136.
Numbers k such that s(j) < s(k) for all j < k, where s = A026136.A026138
Numbers k such that s(j) < s(k) for all j < k, where s = A026136.
a(n) = s(k), where k is the n-th number such that s(j) < s(k) for all j < k, where s = A026136. Also a(n) = 2*t(n) - 1, where t = A026138.A026139
a(n) = s(k), where k is the n-th number such that s(j) < s(k) for all j < k, where s = A026136. Also a(n) = 2*t(n) - 1, where t = A026138.
a(n) = (1/2)*(s(n) - 1), where s = A026139.A026140
a(n) = (1/2)*(s(n) - 1), where s = A026139.
a(n) = (s(n)-s(n-1))/2, where s = A026139.A026141
a(n) = (s(n)-s(n-1))/2, where s = A026139.
Lexicographically earliest permutation of the positive integers such that for n >= 2, |a(n)-n| = [(a(n)+1)/2].A026142
Lexicographically earliest permutation of the positive integers such that for n >= 2, |a(n)-n| = [(a(n)+1)/2].
a(n) = position of n in A026142.A026143
a(n) = position of n in A026142.
Numbers k such that s(j) < s(k) for all j < k, where s = A026142.A026144
Numbers k such that s(j) < s(k) for all j < k, where s = A026142.
a(n) = s(k), where k is the n-th number such that s(j) < s(k) for all j < k, where s = A026142. Also a(n) = 2*t(n) for n >= 2, where t = A026144.A026145
a(n) = s(k), where k is the n-th number such that s(j) < s(k) for all j < k, where s = A026142. Also a(n) = 2*t(n) for n >= 2, where t = A026144.
a(n) = (1/2)*|s(n) - s(n-1)|, where s = A026145.A026146
a(n) = (1/2)*|s(n) - s(n-1)|, where s = A026145.
a(n) = position of n-th 1 in A001285 or A010059 (Thue-Morse sequence).A026147
a(n) = position of n-th 1 in A001285 or A010059 (Thue-Morse sequence).
Irregular triangular array T read by rows: T(n,0) = 1 for i >= 0, T(1,1) = 1,T(2,1) = 1, T(2,2) = 2, T(2,3) = 1, T(2,4) = 1 and for n >= 3, T(n,1) = n-1, T(n,k) = T(n-1,k-2) + T(n-1,k-1) + T(n-1,k) for k=2,...,n+1, and T(n, k+2) = T(n-1, k) + T(n-1, k+1).A026148
Irregular triangular array T read by rows: T(n,0) = 1 for i >= 0, T(1,1) = 1,T(2,1) = 1, T(2,2) = 2, T(2,3) = 1, T(2,4) = 1 and for n >= 3, T(n,1) = n-1, T(n,k) = T(n-1,k-2) + T(n-1,k-1) + T(n-1,k) for k=2,...,n+1, and T(n, k+2) = T(n-1, k) + T(n-1, k+1).
Expansion of 1/((1-2x)(1-5x)(1-10x)(1-11x)).A026149
Expansion of 1/((1-2x)(1-5x)(1-10x)(1-11x)).
a(0) = a(1) = 1; a(n+2) = 2*a(n+1) + 2*a(n).A026150
a(0) = a(1) = 1; a(n+2) = 2*a(n+1) + 2*a(n).
a(n) = T(n,n), where T is the array in A026148.A026151
a(n) = T(n,n), where T is the array in A026148.
a(n) = T(n,n-1), where T is the array in A026148.A026152
a(n) = T(n,n-1), where T is the array in A026148.
T(n,n-2), where T is the array in A026148.A026153
T(n,n-2), where T is the array in A026148.
a(n) = T(n,n-3), where T is the array in A026148.A026154
a(n) = T(n,n-3), where T is the array in A026148.
T(n,n-4), where T is the array in A026148.A026155
T(n,n-4), where T is the array in A026148.
a(n) = T(2n-1,n), where T is the array in A026148.A026156
a(n) = T(2n-1,n), where T is the array in A026148.
a(n) = T(2n,n), where T is the array in A026148.A026157
a(n) = T(2n,n), where T is the array in A026148.
a(n) = T(3n,n), where T is the array in A026148.A026158
a(n) = T(3n,n), where T is the array in A026148.
T(4n,n), where T is the array in A026148.A026159
T(4n,n), where T is the array in A026148.
a(n) = T(2n,n-1), where T is the array in A026148.A026160
a(n) = T(2n,n-1), where T is the array in A026148.