Sequences

392,541 sequences

Number of walks on square lattice. Column y=2 of A052174.A005560
Number of walks on square lattice. Column y=2 of A052174.
Number of walks on square lattice. Column y=3 of A052174.A005561
Number of walks on square lattice. Column y=3 of A052174.
Number of walks on square lattice. Column y=4 of A052174.A005562
Number of walks on square lattice. Column y=4 of A052174.
a(n) = n*(n+2) = (n+1)^2 - 1.A005563
a(n) = n*(n+2) = (n+1)^2 - 1.
Number of n-step walks on square lattice in the first quadrant which finish at distance n-3 from the x-axis.A005564
Number of n-step walks on square lattice in the first quadrant which finish at distance n-3 from the x-axis.
Number of walks on square lattice.A005565
Number of walks on square lattice.
Number of walks of length n on square lattice, starting at origin, staying in first quadrant.A005566
Number of walks of length n on square lattice, starting at origin, staying in first quadrant.
Number of walks on square lattice.A005567
Number of walks on square lattice.
Product of two successive Catalan numbers C(n)*C(n+1).A005568
Product of two successive Catalan numbers C(n)*C(n+1).
Number of walks on square lattice.A005569
Number of walks on square lattice.
Number of walks on cubic lattice.A005570
Number of walks on cubic lattice.
Number of walks on cubic lattice.A005571
Number of walks on cubic lattice.
Number of walks on cubic lattice starting and finishing on the xy plane and never going below it.A005572
Number of walks on cubic lattice starting and finishing on the xy plane and never going below it.
Number of walks on cubic lattice (starting from origin and not going below xy plane).A005573
Number of walks on cubic lattice (starting from origin and not going below xy plane).
Numbers k such that k^2 + 1 is prime.A005574
Numbers k such that k^2 + 1 is prime.
a(n) = A259095(2n,n).A005575
a(n) = A259095(2n,n).
The limiting sequence [A259095(r(r+1)/2-s,r), s=0,1,2,...,r-1] for very large r.A005576
The limiting sequence [A259095(r(r+1)/2-s,r), s=0,1,2,...,r-1] for very large r.
Maxima of the rows of the triangle A259095.A005577
Maxima of the rows of the triangle A259095.
a(2*n) = 2*a(2*n-1), a(2*n+1) = 2*a(2*n)-1.A005578
a(2*n) = 2*a(2*n-1), a(2*n+1) = 2*a(2*n)-1.
a(n) = smallest number k such that Product_{i=1..k} prime(i)/(prime(i)-1) > n.A005579
a(n) = smallest number k such that Product_{i=1..k} prime(i)/(prime(i)-1) > n.
a(n) = smallest number k such that Product_{i=2..k+1} prime(i)/(prime(i)-1) > n.A005580
a(n) = smallest number k such that Product_{i=2..k+1} prime(i)/(prime(i)-1) > n.
a(n) = (n-1)*n*(n+4)/6.A005581
a(n) = (n-1)*n*(n+4)/6.
a(n) = n*(n+1)*(n+2)*(n+7)/24.A005582
a(n) = n*(n+1)*(n+2)*(n+7)/24.
Coefficients of Chebyshev polynomials.A005583
Coefficients of Chebyshev polynomials.
Coefficients of Chebyshev polynomials.A005584
Coefficients of Chebyshev polynomials.
5-dimensional pyramidal numbers: a(n) = n*(n+1)*(n+2)*(n+3)*(2n+3)/5!.A005585
5-dimensional pyramidal numbers: a(n) = n*(n+1)*(n+2)*(n+3)*(2n+3)/5!.
a(n) = n*(n+4)*(n+5)/6.A005586
a(n) = n*(n+4)*(n+5)/6.
a(n) = n*(n+5)*(n+6)*(n+7)/24.A005587
a(n) = n*(n+5)*(n+6)*(n+7)/24.
Number of free binary trees admitting height n.A005588
Number of free binary trees admitting height n.
Number of letters in the US English name of n, excluding spaces and hyphens.A005589
Number of letters in the US English name of n, excluding spaces and hyphens.
a(0) = 0, a(1) = 1, a(2n) = a(n), a(2n+1) = a(n+1) - a(n).A005590
a(0) = 0, a(1) = 1, a(2n) = a(n), a(2n+1) = a(n+1) - a(n).
Number of semigroups of order n with 3 idempotents, considered to be equivalent when they are isomorphic or anti-isomorphic (by reversal of the operator).A005591
Number of semigroups of order n with 3 idempotents, considered to be equivalent when they are isomorphic or anti-isomorphic (by reversal of the operator).
a(n) = F(2n+1) + F(2n-1) - 1.A005592
a(n) = F(2n+1) + F(2n-1) - 1.
a(n) = (F(2n+1) + F(2n-1) + F(n+3) - 2)/2, where F() = Fibonacci numbers A000045.A005593
a(n) = (F(2n+1) + F(2n-1) + F(n+3) - 2)/2, where F() = Fibonacci numbers A000045.
States of a dynamic storage system.A005594
States of a dynamic storage system.
States of a dynamic storage system.A005595
States of a dynamic storage system.
Decimal expansion of Artin's constant Product_{p=prime} (1-1/(p^2-p)).A005596
Decimal expansion of Artin's constant Product_{p=prime} (1-1/(p^2-p)).
Decimal expansion of the twin prime constant C_2 = Product_{ p prime >= 3 } (1-1/(p-1)^2).A005597
Decimal expansion of the twin prime constant C_2 = Product_{ p prime >= 3 } (1-1/(p-1)^2).
a(n) = 1 + Sum_{i=1..n} (n-i+1)*phi(i).A005598
a(n) = 1 + Sum_{i=1..n} (n-i+1)*phi(i).
Running sum of every third term in the {+1,-1}-version of Thue-Morse sequence A010060.A005599
Running sum of every third term in the {+1,-1}-version of Thue-Morse sequence A010060.
Decimal expansion of reciprocal of fine-structure constant alpha.A005600
Decimal expansion of reciprocal of fine-structure constant alpha.
Decimal expansion of proton-to-electron mass ratio.A005601
Decimal expansion of proton-to-electron mass ratio.
Smallest prime beginning a complete Cunningham chain of length n (of the first kind).A005602
Smallest prime beginning a complete Cunningham chain of length n (of the first kind).
Smallest prime beginning a complete Cunningham chain (of the second kind) of length n.A005603
Smallest prime beginning a complete Cunningham chain (of the second kind) of length n.
a(n) = a(n-1)! + a(n-2)!.A005604
a(n) = a(n-1)! + a(n-2)!.
a(n) = a(n-1) + (-1)^(n-1) * a(n-2)^2 for n >= 2 with a(0) = 0 and a(1) = 1.A005605
a(n) = a(n-1) + (-1)^(n-1) * a(n-2)^2 for n >= 2 with a(0) = 0 and a(1) = 1.
Position of first letter of n (in English) in alphabet.A005606
Position of first letter of n (in English) in alphabet.
a(n) = (a(n-1) + a(n-2))!.A005607
a(n) = (a(n-1) + a(n-2))!.
Number of Boolean functions realized by cascades of n gates.A005608
Number of Boolean functions realized by cascades of n gates.
Number of Boolean functions realized by cascades of n gates.A005609
Number of Boolean functions realized by cascades of n gates.