OFFSET
0,47
COMMENTS
T(m,k) is the number of 'carries' that occur when adding k and n-k in base 3 using the traditional addition algorithm.
LINKS
Robert Israel, Table of n, a(n) for n = 0..10010
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.
FORMULA
EXAMPLE
The triangle begins:
0,
0, 0,
0, 0, 0,
0, 1, 1, 0;
0, 0, 1, 0, 0;
0, 0, 0, 0, 0, 0;
0, 1, 1, 0, 1, 1, 0;
0, 0, 1, 0, 0, 1, 0, 0;
0, 0, 0, 0, 0, 0, 0, 0, 0;
0, 2, 2, 1, 2, 2, 1, 2, 2, 0;
MAPLE
A243759:= (m, k) -> padic[ordp](binomial(m, k), 3);
for m from 0 to 50 do
seq(A243759(m, k), k=0..m)
od; # Robert Israel, Jun 15 2014
MATHEMATICA
T[m_, k_] := IntegerExponent[Binomial[m, k], 3];
Table[T[m, k], {m, 0, 12}, {k, 0, m}] // Flatten (* Jean-François Alcover, Jun 05 2022 *)
PROG
(Sage)
m=50
T=[0]+[3^valuation(i, 3) 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]]
[log(Integer(x), base=3) for sublist in Table for x in sublist]
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Tom Edgar, Jun 10 2014
EXTENSIONS
Name clarified by Antti Karttunen, Oct 28 2014
STATUS
approved