Sequences

a(n) = n*a(n-1) + (n-5)*a(n-2).

a(n) = Fibonacci(n+3) - 2.

Numbers k such that 4*k^2 + 1 is prime.

Full reptend primes: primes with primitive root 10.

Cyclic numbers: 10 is a quadratic residue modulo p and class of mantissa is 2.

Primes p such that the congruence 2^x == 3 (mod p) is solvable.

Primes p such that the congruence 2^x = 5 (mod p) is solvable.

(p-1)/x, where p = prime(n) and x = ord(2,p), the smallest positive integer such that 2^x == 1 (mod p).

Least positive primitive root of n-th prime.

Eighth column of quadrinomial coefficients.

Expansion of 1/(1+759*x^2+2576*x^3+759*x^4+x^6).

a(n) = 14*a(n-1) - a(n-2) + 6 for n>1, a(0)=0, a(1)=7.

Numbers k such that 3*k^2 - 3*k + 1 is both a square (A000290) and a centered hexagonal number (A003215).

a(n) = Sum_{k=1..n} k^k.

Apply partial sum operator twice to Fibonacci numbers.

From rook polynomials.

G.f.: (1+x)^2/[(1-x)^4(1-x-x^2)^3].

Number of connected partially ordered sets with n labeled points.

Number of connected topologies with n unlabeled nodes.

Number of connected topologies on n labeled points.

Number of topologies, or transitive digraphs with n unlabeled nodes.

Number of fixed 3-dimensional polycubes with n cells; lattice animals in the simple cubic lattice (6 nearest neighbors), face-connected cubes.

Sum of Fibonacci (A000045) and Pell (A000129) numbers.

Number of chessboard polyominoes with n squares.

Expansion of 1/theta_4(q)^2 in powers of q.

Number of partitions with no even part repeated; partitions of n in which no parts are multiples of 4.

Expansion of q^(-1/4) * (eta(q^4) / eta(q))^2 in powers of q.

Expansion of (psi(x^2) / psi(-x))^3 in powers of x where psi() is a Ramanujan theta function.

Expansion of k/(4*q^(1/2)) in powers of q, where k defined by sqrt(k) = theta_2(0, q)/theta_3(0, q).

Expansion of (psi(-x) / phi(-x))^5 in powers of x where phi(), psi() are Ramanujan theta functions.

Absolute value of coefficients of an elliptic function.

Absolute values of coefficients of an elliptic function.

Expansion of reciprocal of theta series of Leech lattice.

Expansion of reciprocal of theta series of E_8 lattice.

Numbers that are the sum of 4 distinct squares: of form w^2 + x^2 + y^2 + z^2 with 0 <= w < x < y < z.

a(n+6) = -a(n+5) + a(n+4) + 3a(n+3) + a(n+2) - a(n+1) - a(n). a(n) = sign(n) if abs(n)<=3.

a(n) = 11*a(n-1) + a(n-2).

a(n) = Lucas(5*n+2).

These numbers when multiplied by all powers of 4 give the numbers that are not the sums of 4 distinct squares.

Solutions of a fifth-order probability difference equation.

Upper Wythoff sequence (a Beatty sequence): a(n) = floor(n*phi^2), where phi = (1+sqrt(5))/2.

A Beatty sequence: a(n) = floor(n*sqrt(2)).

A Beatty sequence: a(n) = floor(n*(2 + sqrt(2))).

a(n) = floor((n + 1/2) * sqrt(2)).

a(n) = floor((n+1/2)*(2+sqrt(2))); winning positions in the 2-Wythoff game.

Beatty sequence of 1 + 1/sqrt(11).

Beatty sequence of (5+sqrt(13))/2.

u-pile positions in the 3-Wythoff game with i=1.

v-pile numbers of the 3-Wythoff game with i=1.

u-pile numbers for the 3-Wythoff game with i=2.