

A228539


Rows of binary Walsh matrices interpreted as reverse binary numbers.


3



0, 0, 2, 0, 10, 12, 6, 0, 170, 204, 102, 240, 90, 60, 150, 0, 43690, 52428, 26214, 61680, 23130, 15420, 38550, 65280, 21930, 13260, 39270, 4080, 42330, 49980, 27030, 0, 2863311530, 3435973836, 1717986918, 4042322160, 1515870810, 1010580540
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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.
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 ...
Most of these numbers are divisible by Fermat numbers (A000215): All entries in all rows beginning with row n are divisible by F_(n1), except the entries 2^(n1)...2^n1. (This is the same in A228540.)


LINKS

Tilman Piesk, Rows 0..8 of the triangle, flattened
Tilman Piesk, Prime factorizations
Tilman Piesk, Binary Walsh matrix of size 256


FORMULA

T(n,k) + A228540(n,k) = 2^2^n  1
T(n,2^n1) = A122570(n+1)


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
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.


CROSSREFS

A228540 (the same for the negated binary Walsh matrix).
A000215 (Fermat numbers), A023394 (Prime factors of Fermat numbers).
Sequence in context: A213322 A151887 A070681 * A061189 A019220 A019140
Adjacent sequences: A228536 A228537 A228538 * A228540 A228541 A228542


KEYWORD

nonn,tabf


AUTHOR

Tilman Piesk, Aug 24 2013


STATUS

approved



