Sequences

Number of planted identity trees where non-root, non-leaf nodes an even distance from root are of degree 2.

Number of asymmetric rooted connected graphs where every block is a complete graph.

Number of planted trees where non-root, non-leaf nodes an even distance from root are of degree 2.

Number of rooted connected graphs where every block is a complete graph.

Shifts left when INVERT transform applied thrice.

Number of Go games with n moves.

a(n+1) = (2n+3)*a(n) - 2n*a(n-1) + 8n, a(0) = 1, a(1) = 3.

Knopfmacher expansion of 1/2: a(n+1) = a(n-1)(a(n)+1)-1.

Knopfmacher expansion of 2/3: a(n+1) = a(n-1)(a(n)+1)-1.

Number of nodes in regular n-gon with all diagonals drawn.

a(n) = F(F(n)), where F is a Fibonacci number.

a(n) = largest prime factor of n^n + 1.

Generalization of the golden ratio (expansion of (5-13x)/((1+x)(1-4x))).

a(n) is the number of base numbers with 2n+1 digits in the asymmetric families of palindromic squares.

Patterns in a dual ring.

Number of stable towers of 2 X 2 LEGO blocks.

Number of solutions to k_1 + 2*k_2 + ... + n*k_n = 0, where k_i are from {-1,0,1}, i=1..n.

Number of chess games with n plies (another version).

Number of Young tableaux of height <= 7.

Number of Young tableaux of height <= 6.

Number of Young tableaux of height <= 8.

a(n) = (2^n+1)*(2^n+2)/6.

a(n) = 2^(n-1)*(1+2^n).

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

9-gonal (or enneagonal) pyramidal numbers: a(n) = n*(n+1)*(7*n-4)/6.

10-gonal (or decagonal) pyramidal numbers: a(n) = n*(n + 1)*(8*n - 5)/6.

11-gonal (or hendecagonal) pyramidal numbers: a(n) = n*(n+1)*(3*n-2)/2.

12-gonal (or dodecagonal) pyramidal numbers: a(n) = n*(n+1)*(10*n-7)/6.

Stella octangula numbers: a(n) = n*(2*n^2 - 1).

Dodecahedral surface numbers: a(0)=0, a(1)=1, a(2)=20, thereafter 2*((3*n-7)^2 + 21).

a(n) = floor(n^2/2).

Numbers k such that k^2 + 4 is prime.

Hyperperfect numbers: k = m*(sigma(k) - k - 1) + 1 for some m > 1.

2-hyperperfect numbers: n = 2*(sigma(n) - n - 1) + 1.

Smallest n-hyperperfect number: m such that m=n(sigma(m)-m-1)+1; or 0 if no such number exists.

a(n) = C_n / 2 if n is even or ( C_n + C_((n-1)/2) ) / 2 if n is odd, where C = Catalan numbers (A000108).

Erroneous version of A226909.

Strobogrammatic primes.

Squared Fibonacci numbers: a(n) = F(n)^2 where F = A000045.

a(n+1) = a(n)+a(a(a(..(n-1)..))), depth [ n/2 ].

Minimal number of subsets in a separating family for a set of n elements.

Positions where A007600 increases.

Numbers that are divisible by the product of their digits.

Power-sum numbers: let n = a_1 a_2 ... a_k be a k-digit number; n is a power-sum number if there are exponents e_1 ... e_m such that n = Sum_{i=1..m} Sum_{j=1..k} a_j^e_i.

a(n) = a(n-1) + a(n-1-(number of odd terms so far)).

Sum of digits of n-th prime.

Take 1, skip 2, take 3, etc.

Skip 1, take 2, skip 3, etc.

Nonnegative integers in base -4.

Values taken by the sigma function A000203, listed with multiplicity and in ascending order.