Sequences

a(n) = Sum_{k >= 1} floor(n*phi^(3-k)).

a(n) = Sum_{k >= 1} floor((1+sqrt(2))^(n-k)).

a(n) = Sum_{k>=1} floor( 2*(1+sqrt(2))^(n-k) ).

Sum of Floor[ 3*(1+sqrt(2))^(n-k) ] for k from 1 to infinity.

a(n) = Sum_{k >= 1} floor(n*sqrt(2)^(1-k)).

a(n) = Sum_{k>=1} floor(n*sqrt(2)^(2-k)).

a(n) = Sum_{k >=1} floor(n*sqrt(2)^(3-k)).

Expansion of 1/((1-7*x)*(1-8*x)*(1-11*x)).

Expansion of 1/((1-7*x)*(1-8*x)*(1-12*x)).

Expansion of 1/((1-7*x)*(1-9*x)*(1-10*x)).

Expansion of 1/((1-7*x)*(1-9*x)*(1-11*x)).

Expansion of 1/((1-7*x)*(1-9*x)*(1-12*x)).

Expansion of 1/((1-7*x)*(1-10*x)*(1-11*x)).

Expansion of 1/((1-7*x)*(1-10*x)*(1-12*x)).

Expansion of 1/((1-7*x)*(1-11*x)*(1-12*x)).

Expansion of 1/((1-8*x)*(1-9*x)*(1-10*x)).

Expansion of 1/((1-8*x)*(1-9*x)*(1-11*x)).

Expansion of 1/((1-8*x)*(1-9*x)*(1-12*x)).

Expansion of 1/((1-8*x)*(1-10*x)*(1-11*x)).

Expansion of 1/((1-8*x)*(1-10*x)*(1-12*x)).

Expansion of 1/((1-8*x)*(1-11*x)*(1-12*x)).

Expansion of 1/((1-9*x)*(1-10*x)*(1-11*x)).

Expansion of 1/((1-9*x)*(1-10*x)*(1-12*x)).

Expansion of 1/((1-9*x)*(1-11*x)*(1-12*x)).

The Rudin-Shapiro or Golay-Rudin-Shapiro sequence (coefficients of the Shapiro polynomials).

a(n) = n-th partial sum of Golay-Rudin-Shapiro sequence A020985.

Zero-one version of Golay-Rudin-Shapiro sequence (or word).

a(n) = (2/3)*(4^n-1).

a(n) = (5*4^n - 2)/3.

a(n) = Sum_{k=0..n} (-1)^k*A020985(k).

Largest value of k for which Golay-Rudin-Shapiro sequence A020986(k) = n.

a(n) = a(n-1) + a(n-2) + a(n-3), with a(0) = 0, a(1) = 2, a(2) = 1.

List of scores that can be achieved with four darts all of which hit a dartboard with regions labeled 1, 5, 10, 25.

Primes that are both left-truncatable and right-truncatable.

Numbers k such that the sum of the digits of Fibonacci(k) is k.

Numbers k such that the sum of the digits of Fibonacci(k) in base 12 is k.

Numbers n such that the sum of the digits of Lucas(n) is n.

Numbers n such that the sum of the digits of Lucas(n) in base 12 is n.

Conjectured number of irreducible multiple zeta values of depth n and weight 3n (confirmed up to n=7).

Duplicate of A020727.

Pisot sequence P(2,9).

Decimal expansion of zeta(2)*zeta(3)*zeta(4)*...

a(n) = (n/2)*(n^4 + 1).

Pisot sequence P(4,10).

Let q_k=p(p+2) be product of k-th pair of twin primes; sequence gives values of p such that (q_k)^2 > q_{k-i}q_{k+i} for all 1 <= i <= k-1.

Pisot sequence P(4,11), a(0)=4, a(1)=11, a(n+1) is the nearest integer to a(n)^2/a(n-1). Evidently satisfies a(n) = 2*a(n-1)+2*a(n-2).

Let q_k = p*(p+2) be product of k-th pair of twin primes; sequence gives values of p+2 such that (q_k)^2 > q_{k-i}*q_{k+i} for all 1 <= i <= k-1.

Pisot sequence P(5,11), a(0)=5, a(1)=11, a(n+1) is the nearest integer to a(n)^2/a(n-1).

Triangle of coefficients of Laguerre polynomials n!*L_n(x) (rising powers of x).

Triangle of coefficients of Laguerre polynomials L_n(x) (powers of x in decreasing order).