[seqfan] An idea of sequence of sequences concerning with triangle

Vladimir Shevelev shevelev at bgu.ac.il
Sat Nov 8 16:58:37 CET 2014


Dear seqfans,

Let us start with triangle of 1's

1
11
111
1111
....

Reading it in binary and converting to decimal, we obtain
Mersenne numbers (A000225): 1,3,7,15,31,63,127,...
Numbering 1's in triangle consecutively, let us change
every second 1's by 0. We get triangle

1
01
010
1010
....
Again converting rows to decimal, we have sequence
1,1,2,10,21,21,42,...
Further, we change every third entry in the second triangle
by opposite (i.e., 1->0, 0->1):
1
00
011
1000
....
and get sequence  1,0,3,8,28,28,56,...
Changing here every fourth entry by opposite , we get 
sequence 1,0,7,12,20,62,41,..., etc.
Instead of using the sequence "second,third,fourth,...",
we can use "a_2-th, a_3-th,..." for any sequence {a_n(>1)}.

Best regards,
Vladimir


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