|
|
|
|
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 4, 4, 4, 1, 1, 1, 4, 4, 1, 1, 1, 1, 1, 4, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 4, 4, 4, 1, 4, 4, 4, 1, 1, 1, 4, 4, 1, 1, 4, 4, 1, 1, 1, 1, 1, 4, 1, 1, 1, 4, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 4, 4, 4, 1, 4, 4, 4, 1, 4, 4, 4, 1
(list;
table;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,12
|
|
COMMENTS
|
The exponent of T(n,k) is the number of 'carries' that occur when adding k and n-k in base 4 using the traditional addition algorithm.
If T(n,k) != 0 mod 4, then n dominates k in base 4.
|
|
LINKS
|
Tyler Ball, Tom Edgar, and Daniel Juda, Dominance Orders, Generalized Binomial Coefficients, and Kummer's Theorem, Mathematics Magazine, Vol. 87, No. 2, April 2014, pp. 135-143.
Tyler Ball and Daniel Juda, Dominance over N, Rose-Hulman Undergraduate Mathematics Journal, Vol. 13, No. 2, Fall 2013.
|
|
FORMULA
|
|
|
EXAMPLE
|
The triangle begins:
1;
1, 1;
1, 1, 1;
1, 1, 1, 1;
1, 4, 4, 4, 1;
1, 1, 4, 4, 1, 1;
1, 1, 1, 4, 1, 1, 1;
1, 1, 1, 1, 1, 1, 1, 1;
1, 4, 4, 4, 1, 4, 4, 4, 1;
1, 1, 4, 4, 1, 1, 4, 4, 1, 1;
1, 1, 1, 4, 1, 1, 1, 4, 1, 1, 1;
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1;
|
|
PROG
|
(Sage)
m=50
T=[0]+[4^valuation(i, 4) for i in [1..m]]
Table=[[prod(T[1:i+1])/(prod(T[1:j+1])*prod(T[1:i-j+1])) for j in [0..i]] for i in [0..m-1]]
[x for sublist in Table for x in sublist]
|
|
CROSSREFS
|
|
|
KEYWORD
|
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|