Sequences

Theta series of laminated lattice LAMBDA_11^{min}.

Theta series of laminated lattice LAMBDA_11^{max}.

Theta series of laminated lattice LAMBDA_12^{min}.

Theta series of laminated lattice LAMBDA_12^{mid}.

Theta series of laminated lattice LAMBDA_12^{max}.

Theta series of laminated lattice LAMBDA_13^{min}.

Theta series of laminated lattice LAMBDA_13^{mid}.

Theta series of laminated lattice LAMBDA_13^{max}.

a(n) = binomial(n+3, 3)/4 for odd n, n*(n+2)*(n+4)/24 for even n.

Write down all the prime divisors in previous term.

At each step, record how many 1's, 2's, etc. have been seen so far in the sequence.

Diagonals of Pascal's triangle mod 2 interpreted as binary numbers.

Expansion of 1/eta(q)^24; Fourier coefficients of T_{14}.

Number of connected trivalent graphs with 2n nodes and with girth exactly 3.

Number of connected trivalent graphs with 2n nodes and girth exactly 4.

Number of connected trivalent graphs with 2n nodes and girth exactly 5.

Number of connected trivalent graphs with 2n nodes and girth exactly 6.

Number of connected trivalent graphs with 2n nodes and girth exactly 7.

a(n) = length of (n+1)st run, with initial terms 1, 2.

From analyzing an algorithm.

Binomial transform of rooted tree numbers.

Least Carmichael number with n prime factors, or 0 if no such number exists.

Number of permutations of [n] with at least one strong fixed point (a permutation p of {1,2,...,n} is said to have j as a strong fixed point if p(k) < j for k < j and p(k) > j for k > j).

'Eban' numbers (the letter 'e' is banned!).

A series for Pi.

Even pseudoprimes (or primes) to base 2: even numbers k that divide 2^k - 2.

Moebius transform of numbers of preferential arrangements.

Convert the last term from decimal to binary! a(1)=10.

Convert the last term from decimal to binary! a(1)=3.

Chernoff sequence: a(n) = Product_{k=1..n} prime(k)^(n-k+1).

Rows of Pascal's triangle mod 3.

Expansion of Pi in base 8.

Number of segments used to represent n on calculator display, variant 5: digits '6', '7' and '9' use 6, 3 and 6 segments, respectively.

Rows of Sierpiński's triangle (Pascal's triangle mod 2).

Number of letters in the n-th ordinal number (in American English).

Smallest odd composite number that requires n Miller-Rabin primality tests.

Independence number of de Bruijn graph of order n on two symbols.

Two-rowed truncated monotone triangles.

Number of zero-entropy permutations of length n.

A well-behaved cousin of the Hofstadter sequence: a(n) = a(n - 1 - a(n-1)) + a(n - 2 - a(n-2)) for n > 2 with a(0) = a(1) = a(2) = 1.

G.f.: Product_{k>=1} (1 + x^(2*k - 1)) / (1 - x^(2*k)).

Number of conjugacy classes in GL(n,2).

Number of conjugacy classes in GL(n,3).

a(n) = denominator of Bernoulli(2n)/(2n).

Denominators of Bernoulli numbers B_0, B_1, B_2, B_4, B_6, ...

Denominator of (2n+1) B_{2n}, where B_n are the Bernoulli numbers.

Denominator of (2n+1)(2n+2) B_{2n}, where B_n are the Bernoulli numbers. Also denominators of the asymptotic expansion of the polygamma function psi'''(z).

Self-convolution of numbers of preferential arrangements.

Number of parallelogram polyominoes with n cells (also called staircase polyominoes, although that term is overused).

Number of labeled M-type rooted trees on n nodes.