OEIS
A list of number sequences from OEIS appearing in the book.
- p. 11, A000225, $2^n - 1$. (Sometimes called Mersenne numbers, although that name is usually reserved for A001348.)
- p. 12, A000045, Fibonacci numbers: $F_n = F_{n-1} + F_{n-2}$ with $F_0 = 0$ and $F_1 = 1$.
- p. 12, A000032, Lucas numbers (beginning at 2): $L_n = L_{n-1} + L_{n-2}$. (Cf. A000204.)
- p. 35, A000217, Triangular numbers: $a_n = C_{n+1,2} = n(n+1)/2 = 0+1+2+...+n$.
- p. 46, A000292, Tetrahedral (or triangular pyramidal) numbers: $a_n = C_{n+2,3} = n*(n+1)*(n+2)/6$.
- p. 56, A051049, Number of moves needed to solve an n-ring baguenaudier if the two end rings can be moved simultaneously.
- p. 56, A000975, $a_{2n} = 2a_{2n-1}$, $a_{2n+1} = 2a_{2n}+1$ (also $n$-th number without consecutive equal binary digits).
- p. 56, A001045, Jacobsthal sequence (or Jacobsthal numbers): $a_n = a_{n-1} + 2a_{n-2}$, with $a_0 = 0, a_1 = 1$.
- p. 59, A010036, Sum of $2^n, \ldots, 2^{(n+1)} - 1$.
- p. 61, A001511, The ruler function: $2^{a(n)}$ divides $2n$. Or, $a(n) = 2$-adic valuation of $2n$.
- p. 61, A007814, Exponent of highest power of $2$ dividing $n$, a.k.a. the binary carry sequence, the ruler sequence, or the $2$-adic valuation of $n$.
- p. 63, A014577, The regular paper-folding (or dragon curve) sequence.
- p. 79, A010060, Thue-Morse sequence: let $A_k$ denote the first $2^k$ terms; then $A_0 = 0$ and for $k >= 0$, $A_{k+1} = A_k B_k$, where $B_k$ is obtained from $A_k$ by interchanging $0$'s and $1$'s.
- p. 79, A035263, Trajectory of $1$ under the morphism $1 \rightarrow 10$, $0 \rightarrow 11$.
- p. 79, A096268, Period-doubling sequence: fixed point of the morphism $0 \rightarrow 01$, $1 \rightarrow 00$.
- p. 99, A122983, Binomial transform of aeration of A081294.
- p. 100, A007051, $(3^n + 1)/2$
- p. 100, A016142, Expansion of $1/((1-3x)(1-9x))$.
- p. 115, A002487, Stern's diatomic series (or Stern-Brocot sequence): $a_0 = 0$, $a_1 = 1$; $a_{2n} = a_n$, $a_{2n+1} = a_n + a_{n+1}$.
- p. 117, A107839, $a_n=5a_{n-1}-2a_{n-2}$; $a_0=1$, $a_1=5$.
- p. 172, A000012, The simplest sequence of positive numbers: the all $1$'s sequence.
- p. 178, A052944, $2^n + n - 1$
- p. 183, A007581, $(3\ 2^{n-1} + 2^{2 n-1} + 1)/3$
- p. 209, 282, A180119, $a_n = (n+2)! \sum_1^nk!/(k+2)!$
- p. 243, A051064, $3^{a_n}$ exactly divides $3n$. Or, $3$-adic valuation of $3n$.
- p. 249, A005665, Tower of Hanoi with cyclic moves only.
- p. 251, A035512, Number of unlabeled strongly connected digraphs with $n$ nodes.
- p. 252, A003586, $3$-smooth numbers: numbers of the form $2^i 3^j$ with $i, j >= 0$.
- p. 259, A000108, Catalan numbers: $C_n = \binom {2n} n /(n+1) = (2n)!/(n!(n+1)!)$. Also called Segner numbers.
- p. 282, A032766, Numbers that are congruent to $0$ or $1$ mod $3$.