Read More
Date: 20-1-2020
786
Date: 4-7-2020
570
Date: 18-8-2020
1417
|
Catalan's triangle is the number triangle
(1) |
(OEIS A009766) with entries given by
(2) |
for . Each element is equal to the one above plus the one to the left. The sum of each row is equal to the last element of the next row and also equal to the Catalan number . Furthermore, .
The coefficients also give the number of nonnegative partial sums of 1s and s, denoted by Bailey (1996), who gave the alternate form
(3) |
|||
(4) |
for .
REFERENCES:
Bailey, D. F. "Counting Arrangements of 1's and 's." Math. Mag. 69, 128-131, 1996.
Brualdi, R. A. Introductory Combinatorics, 4th ed. New York: Elsevier, 1997.
Forder, H. G. "Some Problems in Combinatorics." Math. Gaz. 45, 199-201, 1961.
Shapiro, L. W. "A Catalan Triangle." Disc. Math. 14, 83-90, 1976.
Sloane, N. J. A. Sequence A009766 in "The On-Line Encyclopedia of Integer Sequences."
|
|
علامات بسيطة في جسدك قد تنذر بمرض "قاتل"
|
|
|
|
|
أول صور ثلاثية الأبعاد للغدة الزعترية البشرية
|
|
|
|
|
العتبة الحسينية تطلق فعاليات المخيم القرآني الثالث في جامعة البصرة
|
|
|