Sequences

a(n) = (d(n)-r(n))/2, where d = A026060 and r is the periodic sequence with fundamental period (1,0,0,0).

a(n) = (d(n)-r(n))/5, where d = A026060 and r is the periodic sequence with fundamental period (0,0,1,4,0).

dot_product(n,n-1,...2,1)*(6,7,...,n,1,2,3,4,5).

a(n) = (d(n)-r(n))/2, where d = A026063 and r is the periodic sequence with fundamental period (1,1,0,1).

a(n) = (d(n)-r(n))/5, where d = A026063 and r is the periodic sequence with fundamental period (1,4,0,0,0).

dot_product(n,n-1,...2,1)*(7,8,...,n,1,2,3,4,5,6).

a(n) = (d(n)-r(n))/2, where d = A026066 and r is the periodic sequence with fundamental period (1,0,0,0).

(d(n)-r(n))/5, where d = A026066 and r is the periodic sequence with fundamental period (0,3,1,0,1).

a(n) = number of (s(0), s(1), ..., s(n)) such that every s(i) is an integer, s(0) = 0, |s(i) - s(i-1)| = 1 for i = 1,2; |s(i) - s(i-1)| <= 1 for i >= 3, s(n) = 2. Also a(n) = T(n,n-2), where T is the array defined in A024996.

a(n) = number of (s(0), s(1), ..., s(n)) such that every s(i) is an integer, s(0) = 0, |s(i) - s(i-1)| = 1 for i = 1,2; |s(i) - s(i-1)| <= 1 for i >= 3, s(n) = 3. Also a(n) = T(n,n-3), where T is the array defined in A024996.

a(n) = number of (s(0), s(1), ..., s(n)) such that every s(i) is an integer, s(0) = 0, |s(i) - s(i-1)| = 1 for i = 1,2; |s(i) - s(i-1)| <= 1 for i >= 3, s(n) = 4. Also a(n) = T(n,n-4), where T is the array defined in A024996.

a(n) = T(2n-1,n), where T is the array defined in A024996.

T(2n,n), where T is the array defined in A024996.

a(n) = T(3n,n), where T is the array defined in A024996.

a(n) = T(4n,n), where T is the array defined in A024996.

a(n) = T(2n,n-1), where T is the array defined in A024996.

a(n) = T(2n,n+1), where T is the array defined in A024996.

a(n) = T(n,[ n/2 ]), where T is the array defined in A024996.

a(n) = Sum_{k = 1..n} T(k,k-1), where T is the array defined in A024996.

Sum{T(n,k)}, k = 0,1,...,n, where T is the array defined in A024996.

Integers in reverse alphabetical order in U.S. English.

Irregular triangular array T read by rows: T(n,k) = C(n,k) for k=0..n for n = 0,1,2,3. For n >= 4, T(n,0) = T(n,2n)=1, T(n,1) = T(n,2n-1) = n - 3, T(4,2) = 4, T(4,3) = 3, T(4,4) = 6; T(4,5) = 3, T(4,6)=4; for n >= 5, T(n,k) = T(n-1,k-2) + T(n-1,k-1) + T(n-1,k) for k=2..2n-2.

a(n) = number of (s(0), s(1), ..., s(n)) such that every s(i) is an integer, s(0) = 0 = s(n), |s(i) - s(i-1)| = 1 for i = 1,2,3; |s(i) - s(i-1)| <= 1 for i >= 4. Also a(n) = T(n,n), where T is the array defined in A026082.

a(n) = number of (s(0), s(1), ..., s(n)) such that every s(i) is an integer, s(0) = 0, |s(i) - s(i-1)| = 1 for i = 1,2,3; |s(i) - s(i-1)| <= 1 for i >= 4, s(n) = 1. Also a(n) = T(n,n-1), where T is the array defined in A026082.

a(n) = number of (s(0), s(1), ..., s(n)) such that every s(i) is an integer, s(0) = 0, |s(i) - s(i-1)| = 1 for i = 1,2,3; |s(i) - s(i-1)| <= 1 for i >= 4, s(n) = 2. Also a(n) = T(n,n-2), where T is the array defined in A026082.

Number of (s(0), s(1), ..., s(n)) such that s(0) = 0, |s(i) - s(i-1)| = 1 for i = 1,2,3; |s(i) - s(i-1)| <= 1 for i >= 4, s(n) = 3; also a(n) = T(n,n-3), where T is the array defined in A026082.

a(n) = number of (s(0), s(1), ..., s(n)) such that every s(i) is an integer, s(0) = 0, |s(i) - s(i-1)| = 1 for i = 1,2,3; |s(i) - s(i-1)| <= 1 for i >= 4, s(n) = 4. Also a(n) = T(n,n-4), where T is the array defined in A026082.

a(n) = T(2n-1,n), where T is the array defined in A026082.

a(n) = T(2n,n), where T is the array defined in A026082.

a(n) = T(3n,n), where T is the array defined in A026082.

a(n) = T(4n,n), where T is the array defined in A026082.

a(n) = T(2n,n-1), where T is the array defined in A026082.

T(2n,n+1), where T is the array defined in A026082.

a(n) = T(n,[ n/2 ]), where T is the array defined in A026082.

a(n) = Sum{T(k,k-1)}, k = 1,2,...,n, where T is the array defined in A026082.

Sum{T(n,k)}, k = 0,1,...,n, where T is the array defined in A026082.

a(n) = number of (s(0), s(1), ..., s(n)) such that every s(i) is an integer, s(0) = 0, |s(i) - s(i-1)| = 1 for i = 1,2,3; |s(i) - s(i-1)| <= 1 for i >= 4. Also a(n) = sum of numbers in row n+1 of the array T defined in A026082 and a(n) = 24*3^(n-4) for n >= 4.

Triangular array T read by rows: T(1,1)=1, T(2,1)=3, T(2,2)=2; for n >= 3, T(n,1)=prime(n) and for k=2,3,...,n, T(n,k) = m*prime(n+1-k), where m is the least positive integer such that m*p(n+1-k) is not any T(i,j) for 1<=i<=n-1 nor any T(n,j) for j<=k-1.

Row of A026098 that contains n.

a(n) = number of the column of A026098 that contains n.

T(n,1) + T(n,2) + ... T(n,n), where T is the array in A026098.

a(n) = T(2n-1,n), where T is the array in A026098.

a(n) = T(n,1) + T(n-1,2) + ...+ T(n-k+1,k), where k = floor((n+1)/2) and T is the array defined in A026098.

a(n) = greatest number in row n of A026098 that is not a positive power of 2.

Triangle T read by rows: differences of Motzkin triangle (A026300).

Number of polyhexes of class PF2 (with one catafusene annealated to pyrene).

Second differences of Motzkin numbers (A001006).

Expansion of 1/((1-2*x)*(1-5*x)*(1-9*x)*(1-12*x)).

a(n) = number of (s(0), s(1), ..., s(n)) such that every s(i) is a nonnegative integer, s(0) = 0, s(1) = 1, s(n) = 3, |s(i) - s(i-1)| <= 1 for i >= 2. Also a(n) = T(n,n-3), where T is the array defined in A026105.

a(n) = number of (s(0), s(1), ..., s(n)) such that every s(i) is a nonnegative integer, s(0) = 0, s(1) = 1, s(n) = 4, |s(i) - s(i-1)| <= 1 for i >= 2. Also a(n) = T(n,n-4), where T is the array defined in A026105.