Sequences

Number of alternating sign n X n matrices invariant under a quarter turn.

Number of alternating sign 2n+1 X 2n+1 matrices symmetric with respect to both horizontal and vertical axes (VHSASM's).

Number of alternating sign n X n matrices symmetric with respect to both diagonals.

Number of alternating sign n X n matrices that are symmetric about a diagonal.

Number of alternating sign 2n+1 X 2n+1 matrices invariant under all symmetries of the square.

Alternating factorials: n! - (n-1)! + (n-2)! - ... 1!.

a(0) = 1; a(n) = (1 + a(0)^3 + ... + a(n-1)^3)/n (not always integral!).

a(n+1) = (1 + a(0)^4 + ... + a(n)^4 )/(n+1) (not always integral!).

n-th derivative of x^x at 1, divided by n.

Number of fountains of n coins.

Erroneous version of A226999.

Characteristic function of nonprimes: 0 if n is prime, else 1.

Number of labeled rooted trees of subsets of an n-set.

Number of rooted trees with 3 nodes of disjoint sets of labels with union {1..n}. If a node has an empty set of labels then it must have at least two children.

Number of rooted trees with 4 nodes of disjoint sets of labels with union {1..n}. If a node has an empty set of labels then it must have at least two children.

Number of rooted trees with 5 nodes of disjoint sets of labels with union {1..n}. If a node has an empty set of labels then it must have at least two children.

Number of regular graphs with n unlabeled nodes.

Number of connected regular graphs with n nodes.

Number of domino tilings of 4 X (n-1) board.

Smallest number with exactly n divisors.

Orders of simple groups.

a(n) = ceiling(exp((n-1)/2)).

a(n) = floor(e^((n-1)/2)).

a(n) = n*2^(n-1) + 1.

Self-contained numbers: odd numbers k whose Collatz sequence contains a higher multiple of k.

Hofstadter Q-sequence: a(1) = a(2) = 1; a(n) = a(n-a(n-1)) + a(n-a(n-2)) for n > 2.

a(n) is the number of integers m which take n steps to reach 1 in '3x+1' problem.

a(n) = a(floor(n/2)) + n; also denominators in expansion of 1/sqrt(1-x) are 2^a(n); also 2n - number of 1's in binary expansion of 2n.

Armstrong (or pluperfect, or Plus Perfect, or narcissistic) numbers: m-digit nonnegative numbers equal to sum of the m-th powers of their digits.

Number of n-term 2-sided generalized Fibonacci sequences.

Central quadrinomial coefficients: largest coefficient of (1 + x + x^2 + x^3)^n.

Central pentanomial coefficients: largest coefficient of (1 + x + ... + x^4)^n.

Finite difference measurements.

a(n) is the number of alpha-labelings of graphs with n edges.

Number of balanced symmetric graphs.

Number of forests with n unlabeled nodes.

a(n) = Sum_t t*F(n,t), where F(n,t) (see A095133) is the number of forests with n (unlabeled) nodes and exactly t trees.

a(n) = Sum_t t*F(n,t), where F(n,t) (see A033185) is the number of rooted forests with n (unlabeled) nodes and exactly t rooted trees.

a(n) is the number of forests with n (unlabeled) nodes in which each component tree is planted, that is, is a rooted tree in which the root has degree 1.

a(n) = Sum_t t*F(n,t), where F(n,t) is the number of forests with n (unlabeled) nodes and exactly t trees, all of which are planted (that is, rooted trees in which the root has degree 1).

Total number of fixed points in rooted trees with n nodes.

Total number of fixed points in trees with n nodes.

Total number of fixed points in planted trees with n nodes.

Fibonacci numbers (or rabbit sequence) converted to decimal.

Coding a recurrence.

Coding Fibonacci numbers.

Hofstadter G-sequence: a(0) = 0; a(n) = n - a(a(n-1)) for n > 0.

a(n) = (F(2*n-1) + F(n+1))/2 where F(n) is a Fibonacci number.

Operator-oriented complexity of n, i.e., the minimum number of occurrences of +, *, and ^ needed to build n from a supply of ones.

Multilevel sieve: at k-th step, accept k numbers, reject k, accept k, ...