Sequences

If any even power of 2 ends with k 1's and 8's, they must be the first k terms of this sequence in reverse order.

If any power of 2 ends with k 3's and 8's, they must be the first k terms of this sequence in reverse order.

If any power of 2 ends with k 5's and 8's, they must be the first k terms of this sequence in reverse order.

If any power of 2 ends with k 7's and 8's, they must be the first k terms of this sequence in reverse order.

If any power of 2 ends with k 8's and 9's, they must be the first k terms of this sequence in reverse order.

Number of 0's in binary expansion of n.

Numerator of n*(n-3)*(3*n^2-6*n+2)/(3*(n-1)*(n-2)).

Denominator of n*(n-3)*(3*n^2 - 6*n + 2)/(3*(n-1)*(n-2)).

a(n) = c([ n/2 ]) + c([ n/3 ]) + ... + c([ n/n ]) for n >=3, where a(1) = 1, a(2) = 2 and c(n) = n-th number not in sequence a( ).

a(n) = c([ n/2 ]) + c([ n/3 ]) + ... + c([ n/n ]) for n >=3, where a(1) = 1, a(2) = 3 and c(n) = n-th number not in sequence a( ).

Generalized Catalan Numbers x^2*A(x)^2 -(1-x+x^2+x^3+x^4)*A(x) + 1 =0.

Generalized Catalan Numbers x^2*A(x)^2 -(1-x+x^2+x^3+x^4+x^5)*A(x) + 1 =0.

Generalized Catalan Numbers x^2*A(x)^2 -(1-x+x^2+x^3+x^4+x^5+x^6)*A(x) + 1 =0.

Expansion of (1+2*x+3*x^2+4*x^3+5*x^4)/(1-x-x^2-x^3-x^4-x^5).

Generalized Catalan numbers: a(0) = 1, a(n) = a(n-1) + Sum_{k=1..n-4} a(k) * a(n-k).

a(n) = a(n-1) + Sum_{k=0..n-4} a(k)*a(n-4-k), a(0) = 1. Generalized Catalan Numbers.

Number of Dyck n-paths with ascents and descents of length equal to 1 (mod 4).

Generalized Catalan Numbers x^4*A(x)^2 -(1-x+x^4+x^5)*A(x) +1 =0.

Generalized Catalan Numbers x^4*A(x)^2 -(1-x+x^4+x^5+x^6)*A(x) + 1 =0.

Generalized Catalan Numbers x^4*A(x)^2 -(1-x+x^4+x^5+x^6+x^7)*A(x) + 1 =0.

Generalized Catalan Numbers x^3*A(x)^2 + (x-1)*A(x) + 1 =0.

Number of Dyck n-paths with ascents and descents of length equal to 1 (mod 3).

Generalized Catalan Numbers x^3*A(x)^2 -(1-x+x^3+x^4)*A(x) + 1 =0.

Dying rabbits: a(n) = a(n-1) + a(n-2) - a(n-4).

Dying rabbits: a(n) = a(n-1) + a(n-2) - a(n-5).

Dying rabbits: a(n) = a(n-1) + a(n-2) - a(n-6).

Dying rabbits: a(n) = a(n-1) + a(n-2) - a(n-7).

Dying rabbits: a(n) = a(n-1) + a(n-2) - a(n-8).

Dying rabbits: a(n) = a(n-1) + a(n-2) - a(n-9).

Dying rabbits: a(n) = a(n-1) + a(n-2) - a(n-10).

Dying rabbits: a(n) = a(n-1) + a(n-2) - a(n-11).

Dying rabbits: a(n) = a(n-1) + a(n-2) - a(n-12).

a(n) = n - 1.

a(n) = n-2.

a(n) = n-3.

a(n) = n-4.

a(n) = n-5.

a(n) = n-6.

a(n) = n-7.

a(n) = n-8.

a(n) = n-9.

a(n) = n-10.

a(n) = n-11.

a(n) = n-12.

a(n) = n - 13.

a(n) = n - 14.

a(n) = n-15.

a(n) = n-16.

a(n) = n-17.

a(n) = n-18.