Sequences

392,541 sequences

T(2n-1,n-1), T given by A027157.A027161
T(2n-1,n-1), T given by A027157.
a(n) = T(2n-1,n-2), T given by A027157.A027162
a(n) = T(2n-1,n-2), T given by A027157.
a(n) = T(n,[ n/2 ]), T given by A027157.A027163
a(n) = T(n,[ n/2 ]), T given by A027157.
a(n) = T(n,0) + T(n,1) + ... + T(n,n), T given by A027157.A027164
a(n) = T(n,0) + T(n,1) + ... + T(n,n), T given by A027157.
T(n,0) + T(n,1) + ... + T(n,[ n/2 ]), T given by A027157.A027165
T(n,0) + T(n,1) + ... + T(n,[ n/2 ]), T given by A027157.
a(n) = Sum_{0<=j<=i<=n} A027157(i, j).A027166
a(n) = Sum_{0<=j<=i<=n} A027157(i, j).
a(n) = Sum_{k=0..floor(n/2)} A027157(n-k, k).A027167
a(n) = Sum_{k=0..floor(n/2)} A027157(n-k, k).
Greatest number in row n of array T given by A027157.A027168
Greatest number in row n of array T given by A027157.
a(n) = self-convolution of row n of array T given by A027157.A027169
a(n) = self-convolution of row n of array T given by A027157.
Triangular array T read by rows (4-diamondization of Pascal's triangle). Step 1: t(n,k) = C(n+2,k+1) + C(n+1,k) + C(n+1,k+1) + C(n,k). Step 2: T(n,k) = t(n,k) - t(0,0) + 1. Domain: 0 <= k <= n, n >= 0.A027170
Triangular array T read by rows (4-diamondization of Pascal's triangle). Step 1: t(n,k) = C(n+2,k+1) + C(n+1,k) + C(n+1,k+1) + C(n,k). Step 2: T(n,k) = t(n,k) - t(0,0) + 1. Domain: 0 <= k <= n, n >= 0.
a(n) = A027170(2n, n).A027171
a(n) = A027170(2n, n).
a(n) = (1/2) * A027170(2n, n).A027172
a(n) = (1/2) * A027170(2n, n).
a(n) = A027170(2n, n-1).A027173
a(n) = A027170(2n, n-1).
a(n) = A027170(2n, n-2).A027174
a(n) = A027170(2n, n-2).
a(n) = A027170(2n-1, n-1).A027175
a(n) = A027170(2n-1, n-1).
a(n) = A027170(2n-1, n-2).A027176
a(n) = A027170(2n-1, n-2).
a(n) = A027170(n, floor(n/2)).A027177
a(n) = A027170(n, floor(n/2)).
a(n) = T(n,0) + T(n,1) + ... + T(n,n), T given by A027170.A027178
a(n) = T(n,0) + T(n,1) + ... + T(n,n), T given by A027170.
a(n) = T(n,0) + T(n,1) + ... + T(n,[ n/2 ]), T given by A027170.A027179
a(n) = T(n,0) + T(n,1) + ... + T(n,[ n/2 ]), T given by A027170.
a(n) = Sum_{0<=j<=i<=n} A027170(i, j).A027180
a(n) = Sum_{0<=j<=i<=n} A027170(i, j).
a(n) = Lucas(n+4) - 2*(n+3).A027181
a(n) = Lucas(n+4) - 2*(n+3).
a(n) = self-convolution of row n of array T given by A027170.A027182
a(n) = self-convolution of row n of array T given by A027170.
a(n) = n-th largest even number in array T given by A027170.A027183
a(n) = n-th largest even number in array T given by A027170.
a(n) = (1/2)*(n-th largest even number in array T given by A027170).A027184
a(n) = (1/2)*(n-th largest even number in array T given by A027170).
Triangular array O by rows: O(n,k) = number of partitions of n into an odd number of parts, the least being k.A027185
Triangular array O by rows: O(n,k) = number of partitions of n into an odd number of parts, the least being k.
Triangular array E by rows: E(n,k) = number of partitions of n into an even number of parts, the least being k.A027186
Triangular array E by rows: E(n,k) = number of partitions of n into an even number of parts, the least being k.
Number of partitions of n into an even number of parts.A027187
Number of partitions of n into an even number of parts.
a(n) = number of partitions of n into an odd number of parts, the least being 2; also a(n+2) = number of partitions of n into an even number of parts, each >=2.A027188
a(n) = number of partitions of n into an odd number of parts, the least being 2; also a(n+2) = number of partitions of n into an even number of parts, each >=2.
Number of partitions of n into an odd number of parts, the least being 3; also, a(n+3) = number of partitions of n into an even number of parts, each >=3.A027189
Number of partitions of n into an odd number of parts, the least being 3; also, a(n+3) = number of partitions of n into an even number of parts, each >=3.
Number of partitions of n into an odd number of parts, the least being 4; also, a(n+4) = number of partitions of n into an even number of parts, each >=4.A027190
Number of partitions of n into an odd number of parts, the least being 4; also, a(n+4) = number of partitions of n into an even number of parts, each >=4.
Number of partitions of n into an odd number of parts, the least being 5; also, a(n+5) = number of partitions of n into an even number of parts, each >=5.A027191
Number of partitions of n into an odd number of parts, the least being 5; also, a(n+5) = number of partitions of n into an even number of parts, each >=5.
Number of partitions of n into an odd number of parts, the least being 6; also, a(n+6) = number of partitions of n into an even number of parts, each >=6.A027192
Number of partitions of n into an odd number of parts, the least being 6; also, a(n+6) = number of partitions of n into an even number of parts, each >=6.
Number of partitions of n into an odd number of parts.A027193
Number of partitions of n into an odd number of parts.
Number of partitions of n into an even number of parts, the least being 2; also, a(n+2) = number of partitions of n into an odd number of parts, each >=2.A027194
Number of partitions of n into an even number of parts, the least being 2; also, a(n+2) = number of partitions of n into an odd number of parts, each >=2.
Number of partitions of n into an even number of parts, the least being 3; also, a(n+3) = number of partitions of n into an odd number of parts, each >=3.A027195
Number of partitions of n into an even number of parts, the least being 3; also, a(n+3) = number of partitions of n into an odd number of parts, each >=3.
Number of partitions of n into an even number of parts, the least being 4; also, a(n+4) = number of partitions of n into an odd number of parts, each >=4.A027196
Number of partitions of n into an even number of parts, the least being 4; also, a(n+4) = number of partitions of n into an odd number of parts, each >=4.
Number of partitions of n into an even number of parts, the least being 5; also, a(n+5) = number of partitions of n into an odd number of parts, each >=5.A027197
Number of partitions of n into an even number of parts, the least being 5; also, a(n+5) = number of partitions of n into an odd number of parts, each >=5.
Number of partitions of n into an even number of parts, the least being 6; also, a(n+6) = number of partitions of n into an odd number of parts, each >=6.A027198
Number of partitions of n into an even number of parts, the least being 6; also, a(n+6) = number of partitions of n into an odd number of parts, each >=6.
Triangular array T read by rows: T(n,k) = number of partitions of n into an odd number of parts, each >=k.A027199
Triangular array T read by rows: T(n,k) = number of partitions of n into an odd number of parts, each >=k.
Triangular array T read by rows: T(n,k) = number of partitions of n into an even number of parts, each >=k.A027200
Triangular array T read by rows: T(n,k) = number of partitions of n into an even number of parts, each >=k.
a(n) = self-convolution of row n of array T given by A026714.A027201
a(n) = self-convolution of row n of array T given by A026714.
a(n) = Sum_{k=0..n-1} T(n,k) * T(n,k+1), with T given by A026714.A027202
a(n) = Sum_{k=0..n-1} T(n,k) * T(n,k+1), with T given by A026714.
a(n) = Sum_{k=0..n-2} T(n,k) * T(n,k+2), with T given by A026714.A027203
a(n) = Sum_{k=0..n-2} T(n,k) * T(n,k+2), with T given by A026714.
a(n) = Sum_{k=0..n-3} T(n,k) * T(n,k+3), with T given by A026714.A027204
a(n) = Sum_{k=0..n-3} T(n,k) * T(n,k+3), with T given by A026714.
a(n) = Sum_{k=0..n} (k+1) * A026714(n, k).A027205
a(n) = Sum_{k=0..n} (k+1) * A026714(n, k).
Numbers m such that (1+i)^m + i is a Gaussian prime.A027206
Numbers m such that (1+i)^m + i is a Gaussian prime.
Self-convolution of row n of array T given by A026725.A027207
Self-convolution of row n of array T given by A026725.
a(n) = Sum_{k=0..n-1} T(n,k) * T(n,k+1), with T given by A026725.A027208
a(n) = Sum_{k=0..n-1} T(n,k) * T(n,k+1), with T given by A026725.
a(n) = Sum_{k=0..n-2} T(n,k) * T(n,k+2), with T given by A026725.A027209
a(n) = Sum_{k=0..n-2} T(n,k) * T(n,k+2), with T given by A026725.
a(n) = Sum_{k=0..n-3} T(n,k) * T(n,k+3), with T given by A026725.A027210
a(n) = Sum_{k=0..n-3} T(n,k) * T(n,k+3), with T given by A026725.