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%I #21 Oct 28 2021 10:00:47
%S 0,0,2,0,10,12,6,0,170,204,102,240,90,60,150,0,43690,52428,26214,
%T 61680,23130,15420,38550,65280,21930,13260,39270,4080,42330,49980,
%U 27030,0,2863311530,3435973836,1717986918,4042322160,1515870810,1010580540
%N Rows of binary Walsh matrices interpreted as reverse binary numbers.
%C 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.
%C 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.)
%C Divisibility by Fermat numbers:
%C All entries are divisible by F_0 = 3, except those with k = 1.
%C All entries in rows n >= 3 are divisible by F_2 = 17, except those with k = 4..7.
%H Tilman Piesk, <a href="/A228539/b228539.txt">Rows 0..8 of the triangle, flattened</a>
%H Tilman Piesk, <a href="/A228539/a228539.txt">Prime factorizations</a>
%H Tilman Piesk, <a href="http://commons.wikimedia.org/wiki/File:Binary_Walsh_matrix_256.svg">Binary Walsh matrix of size 256</a>
%F T(n,k) + A228540(n,k) = 2^2^n - 1
%F T(n,2^n-1) = A122570(n+1)
%e Binary Walsh matrix of size 4 and row 2 of the triangle:
%e 0 0 0 0 0
%e 0 1 0 1 10
%e 0 0 1 1 12
%e 0 1 1 0 6
%e Triangle starts:
%e k = 0 1 2 3 4 5 6 7 8 9 10 11 ...
%e n
%e 0 0
%e 1 0 2
%e 2 0 10 12 6
%e 3 0 170 204 102 240 90 60 150
%e 4 0 43690 52428 26214 61680 23130 15420 38550 65280 21930 13260 39270 ...
%Y Cf. A228540 (the same for the negated binary Walsh matrix).
%Y Cf. A000215 (Fermat numbers), A023394 (Prime factors of Fermat numbers).
%K nonn,tabf
%O 0,3
%A _Tilman Piesk_, Aug 24 2013
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