Sequences

Binary self or Colombian numbers: numbers that cannot be expressed as the sum of distinct terms of the form 2^k+1 (k>=0), or equivalently, numbers not of form m + sum of binary digits of m.

a(0)=1; thereafter a(n+1) = a(n) + number of 1's in binary representation of a(n).

a(n+1) = a(n) + sum of digits in base 3 representation of a(n), with a(0) = 1.

Base 4 self or Colombian numbers (not of form k + sum of base 4 digits of k).

a(n+1) = a(n) + sum of digits in base 4 representation of a(n), with a(0) = 1.

a(n+1) = a(n) + sum of digits in base 5 representation of a(n).

Base 6 self or Colombian numbers (not of form k + sum of base 6 digits of k).

a(n+1) = a(n) + sum of digits in base 6 representation of a(n).

a(n+1) = a(n) + sum of digits in base 7 representation of a(n).

Base 8 self or Colombian numbers (not of form k + sum of base 8 digits of k).

a(n+1) = a(n) + sum of digits in base 8 representation of a(n).

a(n+1) = a(n) + sum of digits in base 9 representation of a(n).

a(n) = sum of base-6 digits of a(n-1) + sum of base-6 digits of a(n-2); a(0)=0, a(1)=1.

a(n) = sum of base-7 digits of a(n-1) + sum of base-7 digits of a(n-2).

a(n) = sum of base-8 digits of a(n-1) + sum of base-8 digits of a(n-2).

a(n) = sum of base-9 digits of a(n-1) + sum of base-9 digits of a(n-2).

a(n) = sum of digits of a(n-1) + sum of digits of a(n-2); a(0) = 0, a(1) = 1.

Shortest representation of -n in 2's-complement format.

Coordination sequence for net formed by holes in D_4 lattice.

Weight distribution of [16,11,4] extended Hamming code of length 16.

Weight distribution of extended Hamming code of length 32 (or 3rd-order Reed-Muller code).

Weight distribution of extended Hamming code of length 64.

Weight distribution of [128,120,4] extended Hamming code of length 128. This is also the Reed-Muller code RM(5,7).

Weight distribution of extended Hamming code of length 256.

Weight distribution of [15,11,3] Hamming code of length 15 and minimal distance 3.

Weight distribution of d=3 Hamming code of length 31.

Weight distribution of d=3 Hamming code of length 63.

Weight distribution of d=3 Hamming code of length 127.

Weight distribution of [255,247,3] Hamming code of length 255.

Weight distribution of d=4 Hamming code of length 15.

Weight distribution of d=4 Hamming code of length 31.

Weight distribution of d=4 Hamming code of length 63.

Weight distribution of d=4 Hamming code of length 127.

Triangle of Euler-Bernoulli or Entringer numbers.

Weight distribution of d=4 Hamming code of length 255.

log2*(n) (version 1): number of times floor(log_2(x)) is used in floor(log_2(floor(log_2(...(floor(log_2(n)))...)))) = 0.

Prefix (or Levenshtein) codes for natural numbers.

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

a(n) = a(n-1)*a(n-2) with a(0)=1, a(1)=4.

a(n) = a(n-1)*a(n-2) with a(0)=1, a(1)=10.

Maximal size of binary code of length n and asymmetric distance 2.

Spontaneous magnetization coefficients for square lattice spin 1 Ising model.

Spontaneous magnetization coefficients for square lattice spin 2 Ising model.

Spontaneous magnetization coefficients for square lattice spin 3 Ising model.

Spontaneous magnetization coefficients for square lattice spin 3/2 Ising model.

Spontaneous magnetization coefficients for square lattice spin 5/2 Ising model.

Partition function coefficients for square lattice spin 1 Ising model.

Partition function coefficients for square lattice spin 2 Ising model.

Partition function coefficients for square lattice spin 5/2 Ising model.

Partition function coefficients for square lattice spin 3/2 Ising model.