Sequences

392,541 sequences

a(n) = Sum_{k=0..2n-2} T(n,k) * T(n,k+2), with T given by A027082.A027111
a(n) = Sum_{k=0..2n-2} T(n,k) * T(n,k+2), with T given by A027082.
a(n) = Sum_{k=0..2n-3} T(n,k) * T(n,k+3), with T given by A027082.A027112
a(n) = Sum_{k=0..2n-3} T(n,k) * T(n,k+3), with T given by A027082.
Triangular array T given by rows: T(n,0)=1 for n >= 0, T(n,1)=1,T(n,2)=2 for n >= 1 and for n >= 2, T(n,k)=T(n-1,k-3)+T(n-1,k-2)+T(n-1,k-1) for 3<=k<=2n-1, T(n,2n)=T(n-1,2n-3)+T(n-1,2n-2).A027113
Triangular array T given by rows: T(n,0)=1 for n >= 0, T(n,1)=1,T(n,2)=2 for n >= 1 and for n >= 2, T(n,k)=T(n-1,k-3)+T(n-1,k-2)+T(n-1,k-1) for 3<=k<=2n-1, T(n,2n)=T(n-1,2n-3)+T(n-1,2n-2).
a(n) = A027113(n, n+2).A027114
a(n) = A027113(n, n+2).
a(n) = T(n,0) + T(n,1) + ... + T(n,2n), T given by A027113.A027115
a(n) = T(n,0) + T(n,1) + ... + T(n,2n), T given by A027113.
a(n) = A027113(n, n+3).A027116
a(n) = A027113(n, n+3).
a(n) = A027113(n, n+4).A027117
a(n) = A027113(n, n+4).
a(n) = A027113(n, 2n).A027118
a(n) = A027113(n, 2n).
a(n) = A027113(n, 2n-1).A027119
a(n) = A027113(n, 2n-1).
a(n) = A027113(n, 2n-2).A027120
a(n) = A027113(n, 2n-2).
a(n) = A027113(n, 2n-3).A027121
a(n) = A027113(n, 2n-3).
a(n) = A027113(n, 2n-4).A027122
a(n) = A027113(n, 2n-4).
a(n) = A027113(n, 2n-5).A027123
a(n) = A027113(n, 2n-5).
a(n) = A027113(n, 2n-6).A027124
a(n) = A027113(n, 2n-6).
a(n) = A027113(n, 2n-7).A027125
a(n) = A027113(n, 2n-7).
a(n) = A027113(n, 2n-8).A027126
a(n) = A027113(n, 2n-8).
a(n) = A027113(n, 2n-9).A027127
a(n) = A027113(n, 2n-9).
a(n) = A027113(n, 2n-10).A027128
a(n) = A027113(n, 2n-10).
a(n) = T(n,n) + T(n,n+1) + ... + T(n,2n), T given by A027113.A027129
a(n) = T(n,n) + T(n,n+1) + ... + T(n,2n), T given by A027113.
a(n) = Sum_{0<=j<=i<=n} A027113(i, n+j).A027130
a(n) = Sum_{0<=j<=i<=n} A027113(i, n+j).
a(n) = diagonal sum of left justified array T given by A027113.A027131
a(n) = diagonal sum of left justified array T given by A027113.
a(n) = diagonal sum of right justified array T given by A027113.A027132
a(n) = diagonal sum of right justified array T given by A027113.
Greatest number in row n of array T given by A027113.A027133
Greatest number in row n of array T given by A027113.
a(n) = self-convolution of row n of array T given by A027113.A027134
a(n) = self-convolution of row n of array T given by A027113.
a(n) = Sum_{k=0..n} T(n,k) * T(n,2n-k), with T given by A027113.A027135
a(n) = Sum_{k=0..n} T(n,k) * T(n,2n-k), with T given by A027113.
a(n) = Sum_{k=0..n-1} T(n,k) * T(n,2n-k), with T given by A027113.A027136
a(n) = Sum_{k=0..n-1} T(n,k) * T(n,2n-k), with T given by A027113.
a(n) = Sum_{k=0..2n} (k+1) * A027113(n, k).A027137
a(n) = Sum_{k=0..2n} (k+1) * A027113(n, k).
a(n) = Sum_{k=0..2n} (k+1) * A027113(n, 2n-k).A027138
a(n) = Sum_{k=0..2n} (k+1) * A027113(n, 2n-k).
T(n,n+1) + T(n,n+2) + ... + T(n,2n), T given by A027113.A027139
T(n,n+1) + T(n,n+2) + ... + T(n,2n), T given by A027113.
a(n) = Sum_{k=0..n} T(n,k) * T(n,n+k), with T given by A027113.A027140
a(n) = Sum_{k=0..n} T(n,k) * T(n,n+k), with T given by A027113.
a(n) = Sum_{k=0..2n-1} T(n,k) * T(n,k+1), with T given by A027113.A027141
a(n) = Sum_{k=0..2n-1} T(n,k) * T(n,k+1), with T given by A027113.
a(n) = Sum_{k=0..2n-2} T(n,k) * T(n,k+2), with T given by A027113.A027142
a(n) = Sum_{k=0..2n-2} T(n,k) * T(n,k+2), with T given by A027113.
a(n) = Sum_{k=0..2n-3} T(n,k) * T(n,k+3), with T given by A027113.A027143
a(n) = Sum_{k=0..2n-3} T(n,k) * T(n,k+3), with T given by A027113.
Triangular array T given by rows: T(n,0)=1 for n >= 0, T(1,1)=2; for even n >= 2, T(n,k)=T(n-2,k-1)+T(n-1,k-1)+T(n-1,k) for 1<=(odd k)<=n-1 and T(n,k)=T(n-1,k-1)+T(n-1,k) for 2<=(even k)<=n-2, T(n,n)=T(n-1,n-1); for odd n<=3, T(n,k)=T(n,k-1)+T(n-1,k-1)+T(n-1,k) for 1<=(odd k)<=n-2 and T(n,k)=T(n-1,k-1)+T(n-1,k) for 2<=(even k)<=n-1, T(n,n)=T(n-1,n-1)+T(n,n-1).A027144
Triangular array T given by rows: T(n,0)=1 for n >= 0, T(1,1)=2; for even n >= 2, T(n,k)=T(n-2,k-1)+T(n-1,k-1)+T(n-1,k) for 1<=(odd k)<=n-1 and T(n,k)=T(n-1,k-1)+T(n-1,k) for 2<=(even k)<=n-2, T(n,n)=T(n-1,n-1); for odd n<=3, T(n,k)=T(n,k-1)+T(n-1,k-1)+T(n-1,k) for 1<=(odd k)<=n-2 and T(n,k)=T(n-1,k-1)+T(n-1,k) for 2<=(even k)<=n-1, T(n,n)=T(n-1,n-1)+T(n,n-1).
a(n) = A027144(2n, n).A027145
a(n) = A027144(2n, n).
a(n) = A027144(2n, n-1).A027146
a(n) = A027144(2n, n-1).
a(n) = A027144(2n, n-2).A027147
a(n) = A027144(2n, n-2).
a(n) = A027144(2n-1, n-1).A027148
a(n) = A027144(2n-1, n-1).
a(n) = A027144(2n-1, n-2).A027149
a(n) = A027144(2n-1, n-2).
a(n) = A027144(n, floor(n/2)).A027150
a(n) = A027144(n, floor(n/2)).
a(n) = T(n,0) + T(n,1) + ... + T(n,n), T given by A027144.A027151
a(n) = T(n,0) + T(n,1) + ... + T(n,n), T given by A027144.
T(n,0) + T(n,1) + ... + T(n,[ n/2 ]), T given by A027144.A027152
T(n,0) + T(n,1) + ... + T(n,[ n/2 ]), T given by A027144.
a(n) = Sum_{0<=j<=i<=n} A027144(i, j).A027153
a(n) = Sum_{0<=j<=i<=n} A027144(i, j).
a(n) = Sum_{k=0..floor(n/2)} A027144(n-k, k).A027154
a(n) = Sum_{k=0..floor(n/2)} A027144(n-k, k).
Greatest number in row n of array T given by A027144.A027155
Greatest number in row n of array T given by A027144.
Self-convolution of array T given by A027144.A027156
Self-convolution of array T given by A027144.
Triangular array T given T(n,k)=(1/2)*t(n+1,k+1), 0<=k<=n, n >= 0, t given by A027144.A027157
Triangular array T given T(n,k)=(1/2)*t(n+1,k+1), 0<=k<=n, n >= 0, t given by A027144.
a(n) = T(2n,n), T given by A027157.A027158
a(n) = T(2n,n), T given by A027157.
a(n) = T(2n,n-1), T given by A027157.A027159
a(n) = T(2n,n-1), T given by A027157.
a(n) = T(2n,n-2), T given by A027157.A027160
a(n) = T(2n,n-2), T given by A027157.