17073

Properties

Appears in sequences

• Number of free polyominoes (or square animals) with n cells.at n=11A000105
• Number of positive integers <= 2^n of form x^2 + 17 y^2.at n=17A054230
• Number of partitions of n into 5-smooth parts.at n=39A112581
• Triangle read by rows: T(n,k) (n>=1) gives the number of n-indecomposable polyominoes with k cells (k >= n).at n=55A125753
• Triangle read by rows: T(n,k) (n>=1) gives the number of n-indecomposable polyominoes with k cells (k >= n).at n=76A125753
• Triangle read by rows: T(n,k) (n>=1) gives the number of n-indecomposable polyominoes with k cells (k >= n).at n=101A125753
• Triangle read by rows: T(n,k) (n>=1) gives the number of n-indecomposable polyominoes with k cells (k >= 1).at n=55A125761
• Triangle read by rows: T(n,k) (n>=1) gives the number of n-indecomposable polyominoes with k cells (k >= 1).at n=76A125761
• Triangle read by rows: T(n,k) (n>=1) gives the number of n-indecomposable polyominoes with k cells (k >= 1).at n=101A125761
• Triangle of coefficients of polynomials u(n,x) jointly generated with A209169; see the Formula section.at n=49A209168
• Number of free polyominoes with 2n-1 cells.at n=5A210997
• Number of n X 2 arrays of the minimum value of corresponding elements and their horizontal or antidiagonal neighbors in a random, but sorted with lexicographically nondecreasing rows and columns, 0..2 n X 2 array.at n=20A219621
• Triangular array: For n >= 2 and 0 < k <= n - 2, T(n, k) equals the number of (unrooted) duplication trees on n gene segments that are canonical and whose leftmost visible duplication event is (k, r), for 1 <= r <= (n - k)/2.at n=50A264870
• Triangle read by rows: T(n,k) = number of ways, summed over the free n-ominoes, that an n-omino with an assigned orientation can be maximally (partially) covered by k X 1 tiles.at n=55A308437
• The squarefree dual of a multiset partition has, for each vertex, one block consisting of the indices (or positions) of the blocks containing that vertex, counted without multiplicity. Then a(n) is the number of non-isomorphic multiset partitions of weight n whose squarefree dual is strict (no repeated blocks).at n=10A319558
• a(n) = - Sum_{d|n} (-n/d)^d * binomial(d+n/d-1, d).at n=21A338683
• Number of prime polyominoes with n cells.at n=11A342430
• Irregular triangle read by rows: T(n,k) = number of k-sided polygons formed when connecting infinite lines between all vertices and all points that divide the sides of an equilateral triangle into n equal parts, for k = 3, 4, ..., max_k.at n=37A346446
• a(n) is the number of subsets of the divisors of k which sum to k+1 where k is a number all of whose prime divisors are consecutive primes starting at 2.at n=40A359753
• Array read by diagonals downwards: A(n,k) for n>=2 and k>=0 is the number of (n,k)-polyominoes.at n=54A381030