Sequences

a(n) is the smallest m such that A002110(n) + m is prime.

Let k be the exponent of highest power of 2 dividing n (A007814); a(n) = 2^(k+1)-1.

a(n) = n XOR (n-1), i.e., nim-sum of sequential pairs, written in binary.

Pronic numbers repeated 4 times; a(n) = floor(n/4) * ceiling((n+1)/4).

a(n) = floor(n/4)*ceiling((n+2)/4).

a(n) = floor(n/4)*ceiling((n+3)/4).

Triangular array read by rows: T(n,m) = number of ways your team can score m points in n rounds of a soccer competition (loss=0 point, draw=1 point, win=3 points), for n >= 0, 0 <= m <= 3n.

Number of permutations P of {1,2,...,n} such that P(1)=1 and |P^-1(i+1)-P^-1(i)| equals 1 or 2 for i=1,2,...,n-1.

Triangle T(n,k) (0 <= k <= n) giving number of chains of length k in partially ordered set formed from subsets of n-set by inclusion.

a(n) = (n+3)*n!/2.

k=2 column of A038719.

Take the sequence of natural numbers (A000027) and reverse successive subsequences of lengths 1,2,3,4,... .

a(n) = 6*a(n-1) - a(n-2), n >= 2, a(0)=1, a(1)=4.

Each term describes the ordinal number of its position in the sequence, by a summation of the numerals in that ordinal number and then by the differences between each contiguous pair of the numerals in the order in which they appear.

a(n) = 6*a(n-1) - a(n-2), n >= 2, a(0)=1, a(1)=2.

The number of n-step self-avoiding walks in a 5-dimensional hypercubic lattice with no non-contiguous adjacencies.

Configurations of linear chains in a 5-dimensional hypercubic lattice.

Configurations of linear chains in a 5-dimensional hypercubic lattice.

Configurations of linear chains in a 6-dimensional hypercubic lattice.

Path-counting triangular array T(i,j), read by rows, obtained from array t in A038792 by T(i,j) = t(2*i-j, j) (for i >= 1 and 1 <= j <= i).

Number of columns in all directed column-convex polyominoes of area n+1.

T(n,n-3), array T as in A038730.

T(n,n-4), array T as in A038730.

T(n,n-5), array T as in A038730.

T(n,n-6), array T as in A038730.

a(n) = T(3*n + 1, n + 1), array T as in A038792.

T(n,n-2), array T as in A038792.

Path-counting array T(i,j) obtained from array t in A038792 by T(i,j)=t(2i+1,j).

T(n,n-2), array T as in A038738.

a(n) = T(n,n-3), array T as in A038738.

T(n,n-4), array T as in A038738.

T(n,n-5), array T as in A038738.

T(n,n-6), array T as in A038738.

a(n) = T(2n,n), array T as in A038738.

Configurations of linear chains in a 6-dimensional hypercubic lattice.

Coefficients arising in the enumeration of configurations of linear chains.

Coefficients arising in the enumeration of configurations of linear chains.

Coefficients arising in the enumeration of configurations of linear chains.

Coefficients arising in the enumeration of configurations of linear chains.

A variant of the recurrence for A001190.

A variant of the recurrence for A001190.

Earliest sequence where a(a(n))=number of partitions of n.

Nonprime partition numbers.

a(2n) = 3^n, a(2n+1) = 2*3^n.

Earliest sequence where a(a(n))=2^n.

Earliest sequence where a(a(n))=3^n.

Earliest sequence where a(a(n))=4^n.

Number of ways of covering a 2n X 2n lattice by 2n^2 dominoes with exactly 4 horizontal (or vertical) dominoes.

a(n) = ceiling(sqrt(n))*floor(sqrt(n)).

a(n) = n - floor(sqrt(n)) * ceiling(sqrt(n)).