Sequences

Coordination sequence for quartz.

Coordination sequence T1 for Scapolite.

Coordination sequence T2 for Scapolite.

Coordination sequence for tridymite, lonsdaleite, and wurtzite.

Coordination sequence T1 for Zeolite Code ATO.

Coordination sequence T1 for Zeolite Code GIS.

Coordination sequence T1 for Coesite.

Coordination sequence T2 for Coesite.

Number of strings on n symbols in Stockhausen problem.

Total length of strings on n symbols in Stockhausen problem.

Number of performances of n fragments in Stockhausen problem.

Total length of performances of n fragments in Stockhausen problem.

Number of performances of n fragments in Stockhausen problem.

Total length of performances of n fragments in Stockhausen problem.

Triangle read by rows of Stirling numbers of first kind, s(n,k), n >= 1, 1 <= k <= n.

Triangle of Stirling numbers of first kind, s(n, n-k+1), n >= 1, 1 <= k <= n. Also triangle T(n,k) giving coefficients in expansion of n!*binomial(x,n)/x in powers of x.

Triangle of Stirling numbers of the second kind, S2(n,k), n >= 1, 1 <= k <= n.

Reflected triangle of Stirling numbers of 2nd kind, S(n,n-k+1), n >= 1, 1 <= k <= n.

Triangle T(n,k) = n!/(n-k)! (0 <= k <= n) read by rows, giving number of permutations of n things k at a time.

Boustrophedon version of triangle of Euler-Bernoulli or Entringer numbers read by rows.

Triangle of Euler-Bernoulli or Entringer numbers read by rows.

Triangle of Euler-Bernoulli or Entringer numbers read by rows: T(n,k) is the number of down-up permutations of n+1 starting with k+1.

Read across rows of Euler-Bernoulli or Entringer triangle.

Triangle of partition numbers: T(n,k) = number of partitions of n in which the greatest part is k, 1 <= k <= n. Also number of partitions of n into k positive parts, 1 <= k <= n.

Erroneous version of A342587.

Number of different parameter sets for orthogonal arrays with 2^n runs.

Triangle of quadrinomial coefficients, row n is the sequence of coefficients of (1 + x + x^2 + x^3)^n.

Square array of Delannoy numbers D(i,j) (i >= 0, j >= 0) read by antidiagonals.

Triangle read by rows: Q(n,m) = number of partitions of n into m distinct parts, n>=1, m>=1.

Triangle T(n,k) of rencontres numbers (number of permutations of n elements with k fixed points).

Triangle of rencontres numbers.

Triangle of Eulerian numbers T(n,k) (n >= 1, 1 <= k <= n) read by rows.

Triangle of coefficients in expansion of D^n (tan x) in powers of tan x.

Triangle of coefficients in expansion of D^n (sec x) / sec x in powers of tan x.

Triangle read by rows: T(n,k) is the number of partially labeled rooted trees with n vertices, k of which are labeled, 0 <= k <= n.

Triangle of Lehmer-Comtet numbers of the first kind.

Triangle of Lah numbers.

Triangle of D'Arcais numbers.

Triangle T(n,k) of associated Stirling numbers of second kind, n >= 2, 1 <= k <= floor(n/2).

Triangle read by rows: T(n,k) (n >= 0, 0 <= k <= n) gives number of {0,1} n X n matrices with all row and column sums equal to k.

Poupard's triangle: triangle of numbers arising in enumeration of binary trees.

Triangle of Mahonian numbers T(n,k): coefficients in expansion of Product_{i=0..n-1} (1 + x + ... + x^i), where k ranges from 0 to A000217(n-1). Also enumerates permutations by their major index.

Triangle read by rows: T(n,k) (n >= 1, 0 <= k <= ceiling(n/2)-1) = number of permutations of [n] with k peaks.

Triangle read by rows: T(n,k) (n>=1; 1<=k<=n) is the number of permutations of [n] in which the longest increasing run has length k.

Triangle read by rows: T(n,k) = number of permutations of [n] allowing i->i+j (mod n), j=0..k-1.

Triangle T(n,k) read by rows: associated Stirling numbers of first kind (n >= 2, 1 <= k <= floor(n/2)).

Table T(n,k) giving number of permutations of [1..n] with order dividing k, read by antidiagonals.

Triangle of tangent numbers.

Triangle T(n,k) of arctangent numbers: expansion of arctan(x)^n/n!.

Triangle of coefficients of Chebyshev polynomials T_n(x).