Analytic methods applied to a sequence of binomial coefficients
نویسندگان
چکیده
منابع مشابه
Estimating the Sequence of Real Binomial Coefficients
The sequence n 7→ ( a n ) of real binomial coefficients is studied in two main cases: a n and n a. In the first case a uniform approximation with high accuracy is obtained, in contrast to DeMoivre-Laplace approximation, which has essentially local character and is good only for n ≈ a2 . In the second case, for every a ∈ R \ ( N ∪ {−1, 0} ), the functions A(a,m) and B(a,m) are determined, such t...
متن کاملGeometry of Binomial Coefficients
This note describes the geometrical pattern of zeroes and ones obtained by reducing modulo two each element of Pascal's triangle formed from binomial coefficients. When an infinite number of rows of Pascal's triangle are included, the limiting pattern is found to be "self-similar," and is characterized by a "fractal dimension" log2 3. Analysis of the pattern provides a simple derivation of the ...
متن کاملA Sequence of Binomial Coefficients Related to Lucas and Fibonacci Numbers
A positive real sequence (ak) n k=0 is said to be unimodal if there exist integers k0, k1, 0 ≤ k0 ≤ k1 ≤ n such that a0 ≤ a1 ≤ · · · ≤ ak0 = ak0+1 = · · · = ak1 ≥ ak1+1 ≥ · · · ≥ an. The integers l, k0 ≤ l ≤ k1 are called the modes of the sequence. If k0 < k1 then (ak)k=0 is said to have a plateau of k1 − k0 + 1 elements; if k0 = k1 then it is said to have a peak. A real sequence is said to be ...
متن کاملPlanar Binomial Coefficients
The notion of binomial coefficients (T S ) of finite planar, reduced rooted trees T, S is defined and a recursive formula for its computation is shown. The nonassociative binomial formula (1 + x) = ∑
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 1978
ISSN: 0012-365X
DOI: 10.1016/0012-365x(78)90101-2