파스칼_삼각형,Pascal_triangle

Difference between r1.15 and the current

@@ -34,5 +34,6 @@
http://rosettacode.org/wiki/Pascal%27s_triangle (PL 구현)
https://artofproblemsolving.com/wiki/index.php/Pascal%27s_triangle
http://oeis.org/wiki/Pascal_triangle
그리고 (1,1)-Pascal triangle이 Pascal's triangle, (1,2)-Pascal triangle이 Lucas triangle, .... 일반화?
[[https://oeis.org/wiki/(a,b)-Pascal_triangle]]


1
1 1
1 2 1
1 3 3 1
1 4 6 4 1
1 5 10 10 5 1
...

https://i.imgur.com/CeHuBvw.png


${}_n\mathrm{C}_r={}_n\mathrm{C}_{n-r}$ (좌우 대칭)

${}_{n+1}\mathrm{C}_r={}_n\mathrm{C}_{r-1}+{}_n\mathrm{C}_r$


이항정리,binomial_theorem에 의해
(1 + x)n = nC0 + nC1x + nC2x2 + … + nCnxn
x = 1을 대입하면
2n = nC0 + nC1 + … + nCn


수,numbers들의 배열이며, 그 수는 이항계수,binomial_coefficient chk

확장/일반화 by Newton:
https://youtu.be/gMlf1ELvRzc?t=626