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The heptanacci numbers are a generalization of the Fibonacci numbers defined by H_0=0, H_1=1, H_2=1, H_3=2, H_4=4, H_5=8, H_6=16, and the recurrence relation ...

The numbers H_n=H_n(0), where H_n(x) is a Hermite polynomial, may be called Hermite numbers. For n=0, 1, ..., the first few are 1, 0, -2, 0, 12, 0, -120, 0, 1680, 0, ... ...

The hexanacci numbers are a generalization of the Fibonacci numbers defined by H_0=0, H_1=1, H_2=1, H_3=2, H_4=4, H_5=8, and the recurrence relation ...

A real quantity having a value less than zero (<0) is said to be negative. Negative numbers are denoted with a minus sign preceding the corresponding positive number, i.e., ...

The sequence a(n) given by the exponents of the highest power of 2 dividing n, i.e., the number of trailing 0s in the binary representation of n. For n=1, 2, ..., the first ...

The Fibonacci number F_(n+1) gives the number of ways for 2×1 dominoes to cover a 2×n checkerboard, as illustrated in the diagrams above (Dickau). The numbers of domino ...

A prime power is a prime or integer power of a prime. A test for a number n being a prime is implemented in the Wolfram Language as PrimePowerQ[n]. The first few prime powers ...

Vizing's theorem states that a graph can be edge-colored in either Delta or Delta+1 colors, where Delta is the maximum vertex degree of the graph. A graph with edge chromatic ...

A deeper result than the Hardy-Ramanujan theorem. Let N(x,a,b) be the number of integers in [n,x] such that inequality a<=(omega(n)-lnlnn)/(sqrt(lnlnn))<=b (1) holds, where ...

Let a prime number generated by Euler's prime-generating polynomial n^2+n+41 be known as an Euler prime. (Note that such primes are distinct from prime Euler numbers, which ...