Sequences

392,541 sequences

Octal formula for dragon curve of order n.A003460
Octal formula for dragon curve of order n.
Bode numbers multiplied by 10: 4 + 3*floor(2^(n-1)).A003461
Bode numbers multiplied by 10: 4 + 3*floor(2^(n-1)).
a(n) = (3^n - 1)/2.A003462
a(n) = (3^n - 1)/2.
a(n) = (5^n - 1)/4.A003463
a(n) = (5^n - 1)/4.
a(n) = (6^n - 1)/5.A003464
a(n) = (6^n - 1)/5.
Number of ways to cover an n-set.A003465
Number of ways to cover an n-set.
Number of minimal covers of an n-set that have exactly one point which appears in more than one set in the cover.A003466
Number of minimal covers of an n-set that have exactly one point which appears in more than one set in the cover.
Number of minimal covers of an n-set that cover exactly 3 points uniquely.A003467
Number of minimal covers of an n-set that cover exactly 3 points uniquely.
Number of minimal 3-covers of a labeled n-set.A003468
Number of minimal 3-covers of a labeled n-set.
Number of minimal covers of an (n + 1)-set by a collection of n nonempty subsets, a(n) = A035348(n,n-1).A003469
Number of minimal covers of an (n + 1)-set by a collection of n nonempty subsets, a(n) = A035348(n,n-1).
a(n) = n*a(n-1) - a(n-2) + 1 + (-1)^n.A003470
a(n) = n*a(n-1) - a(n-2) + 1 + (-1)^n.
Number of permutations with no hits on 2 main diagonals.A003471
Number of permutations with no hits on 2 main diagonals.
a(n) = 2^(n-4)*C(n,4).A003472
a(n) = 2^(n-4)*C(n,4).
Generalized Euler phi function (for p=2).A003473
Generalized Euler phi function (for p=2).
Generalized Euler phi function (for p=3).A003474
Generalized Euler phi function (for p=3).
Expansion of Sum_{k>0} (-1)^(k+1) q^(k^2) / ((1-q)(1-q^3)(1-q^5)...(1-q^(2k-1))).A003475
Expansion of Sum_{k>0} (-1)^(k+1) q^(k^2) / ((1-q)(1-q^3)(1-q^5)...(1-q^(2k-1))).
a(n) = a(n-1) + 2*a(n-3).A003476
a(n) = a(n-1) + 2*a(n-3).
Expansion of 1/((1-2x)(1+x^2)(1-x-2x^3)).A003477
Expansion of 1/((1-2x)(1+x^2)(1-x-2x^3)).
Expansion of 1/((1-2*x)*(1-x-2*x^3)).A003478
Expansion of 1/((1-2*x)*(1-x-2*x^3)).
Expansion of 1/((1-x)*(1-x-2*x^3)).A003479
Expansion of 1/((1-x)*(1-x-2*x^3)).
a(0) = 1, a(1) = 2, for n > 1, a(n) = 4*a(n-1) - 2*a(n-2).A003480
a(0) = 1, a(1) = 2, for n > 1, a(n) = 4*a(n-1) - 2*a(n-2).
a(n) = 7*a(n-1) - a(n-2) + 5.A003481
a(n) = 7*a(n-1) - a(n-2) + 5.
a(n) = 7*a(n-1) - a(n-2) + 4, with a(0) = 0, a(1) = 5.A003482
a(n) = 7*a(n-1) - a(n-2) + 4, with a(0) = 0, a(1) = 5.
Number of square permutations of n elements.A003483
Number of square permutations of n elements.
Radon function, also called Hurwitz-Radon numbers.A003484
Radon function, also called Hurwitz-Radon numbers.
Hurwitz-Radon function at powers of 2.A003485
Hurwitz-Radon function at powers of 2.
a(n) = (n^2 + 1)*3^n.A003486
a(n) = (n^2 + 1)*3^n.
a(n) = a(n-1)^2 - 2, with a(0) = 5.A003487
a(n) = a(n-1)^2 - 2, with a(0) = 5.
High temperature series for spin-1/2 Ising surface susceptibility on planar hexagonal lattice.A003488
High temperature series for spin-1/2 Ising surface susceptibility on planar hexagonal lattice.
High temperature series for spin-1/2 Ising surface susceptibility on square lattice.A003489
High temperature series for spin-1/2 Ising surface susceptibility on square lattice.
High temperature series for spin-1/2 Ising surface susceptibility on 3-dimensional simple cubic lattice.A003490
High temperature series for spin-1/2 Ising surface susceptibility on 3-dimensional simple cubic lattice.
High temperature series for spin-1/2 Ising surface susceptibility on f.c.c. lattice.A003491
High temperature series for spin-1/2 Ising surface susceptibility on f.c.c. lattice.
High temperature series for spin-1/2 Ising surface susceptibility on b.c.c. lattice.A003492
High temperature series for spin-1/2 Ising surface susceptibility on b.c.c. lattice.
High temperature series for spin-1/2 Ising surface susceptibility on square lattice.A003493
High temperature series for spin-1/2 Ising surface susceptibility on square lattice.
High temperature series for susceptibility for spherical model on b.c.c. lattice.A003494
High temperature series for susceptibility for spherical model on b.c.c. lattice.
High temperature series for susceptibility for spherical model on f.c.c. lattice.A003495
High temperature series for susceptibility for spherical model on f.c.c. lattice.
High temperature series for spherical model internal energy on 3-dimensional simple cubic lattice.A003496
High temperature series for spherical model internal energy on 3-dimensional simple cubic lattice.
Internal energy series for b.c.c. lattice.A003497
Internal energy series for b.c.c. lattice.
High temperature series for internal energy for spherical model on f.c.c. lattice.A003498
High temperature series for internal energy for spherical model on f.c.c. lattice.
a(n) = 6*a(n-1) - a(n-2), with a(0) = 2, a(1) = 6.A003499
a(n) = 6*a(n-1) - a(n-2), with a(0) = 2, a(1) = 6.
a(n) = 4*a(n-1) - a(n-2) with a(0) = 2, a(1) = 4.A003500
a(n) = 4*a(n-1) - a(n-2) with a(0) = 2, a(1) = 4.
a(n) = 5*a(n-1) - a(n-2), with a(0) = 2, a(1) = 5.A003501
a(n) = 5*a(n-1) - a(n-2), with a(0) = 2, a(1) = 5.
The smaller of a betrothed pair.A003502
The smaller of a betrothed pair.
The larger of a betrothed pair.A003503
The larger of a betrothed pair.
a(0)=a(1)=1; thereafter a(n+1) = (1/n)*Sum_{k=0..n} a(k)^2 (a(n) is not always integral!).A003504
a(0)=a(1)=1; thereafter a(n+1) = (1/n)*Sum_{k=0..n} a(k)^2 (a(n) is not always integral!).
Number of simple tournaments with n nodes.A003505
Number of simple tournaments with n nodes.
Triangle of denominators in Leibniz's Harmonic Triangle a(n,k), n >= 1, 1 <= k <= n.A003506
Triangle of denominators in Leibniz's Harmonic Triangle a(n,k), n >= 1, 1 <= k <= n.
Number of rigid tournaments with n nodes.A003507
Number of rigid tournaments with n nodes.
a(1) = 1; for n>1, a(n) = a(n-1) + 1 + sum of distinct prime factors of a(n-1) that are < a(n-1).A003508
a(1) = 1; for n>1, a(n) = a(n-1) + 1 + sum of distinct prime factors of a(n-1) that are < a(n-1).
a(n) is the index of the first occurrence of n in A155934(m) = k(m) = the least integer such that every m X m (0,1)-matrix with exactly k(m) ones in each row and in each column contains a 2 X 2 submatrix without zeros.A003509
a(n) is the index of the first occurrence of n in A155934(m) = k(m) = the least integer such that every m X m (0,1)-matrix with exactly k(m) ones in each row and in each column contains a 2 X 2 submatrix without zeros.