OFFSET
0,3
COMMENTS
T(n,k) is row k of the binary Walsh matrix of size 2^n read as reverse binary number. The left digit is always 0, so all entries are even.
Most of these numbers are divisible by Fermat numbers (A000215): All entries in all rows beginning with row n are divisible by F_(n-1), except the entries 2^(n-1)...2^n-1. (This is the same in A228540.)
Divisibility by Fermat numbers:
All entries are divisible by F_0 = 3, except those with k = 1.
All entries in rows n >= 3 are divisible by F_2 = 17, except those with k = 4..7.
LINKS
Tilman Piesk, Rows 0..8 of the triangle, flattened
Tilman Piesk, Prime factorizations
Tilman Piesk, Binary Walsh matrix of size 256
EXAMPLE
Binary Walsh matrix of size 4 and row 2 of the triangle:
0 0 0 0 0
0 1 0 1 10
0 0 1 1 12
0 1 1 0 6
Triangle starts:
k = 0 1 2 3 4 5 6 7 8 9 10 11 ...
n
0 0
1 0 2
2 0 10 12 6
3 0 170 204 102 240 90 60 150
4 0 43690 52428 26214 61680 23130 15420 38550 65280 21930 13260 39270 ...
CROSSREFS
KEYWORD
nonn,tabf
AUTHOR
Tilman Piesk, Aug 24 2013
STATUS
approved