EricD./0and1pattern

[Eric]

Hello

first i consider :
2=01010101010101010101...
3=001001001001001001001001001001...
4=00010001000100010001000100010001...


i make sum of 2 and 3 and i have the pattern
010101
001001

sum of 2,3,4 and i have the pattern
010101010101
001001001001
000100010001

each time i have a pattern of a "n" numbers of columns (as width)
and as length (6,12,30,42,56,...) A002378  Oblong (or pronic, or
heteromecic) numbers: n(n+1)

so n*n*(n+1)=n^3+n^2 which is A011379  n^2+n^3.

for each pattern i consider the number of 0 and the number of 1,
number of 0 | 7|23|55|107|194
number of 1 | 5|13|25|43|58
with A011379 as tool i can go faster

i make a search for 7|23|55|107|194...i have 6821 results
i make a search for 5|13|25|43|58...i have 8528 results  lol :o)
...i'm very proud of my search lol   (joke)...

but for 7,23,55,107,194 and 5,13,25,43,58 i found nothing in database
i try with subtraction of each term (23-7,55-23,etc...),
there are some results but i dont see all of them in detail presently...

however,
for each pattern, more than the number of zero, i will see if there is some
scheme (only for eyes pleasure without conviction)

And
we can take away a crescent quantity of 0,
by subtract two times A000217   Triangular numbers: a(n) = C(n+1,2) =
n(n+1)/2 = 0+1+2+...+n. for each pattern this is the first "triangular hat"
of 0...and second "triangular hat" of 0

and for the 1 numbers i can subtract n*1 of each pattern

it give
number of 0 | 7|23|55|107|194
minus 	  3| 6|10| 15| 21
		  4|17|45| 92|173 i have 2 results in database and this is NOT A095667
minus 	  3|6 |10| 15| 21
		  1|11|55| 77|152  i find nothing in database

number of 1 | 5|13|25|43|58
minus 	  2| 3| 4| 5| 6
		  3|10|21|38|52 i find nothing in database

that's all for this mail
it was just to play with 1 and 0...
i hope my step is not tasteless
and that i dont fall in a trap of trivial properties of numbers.
(i fear for one's bacon lol)

PS : using the "|" caracter to separate numbers is not very efficient but i
try it to test, and i'm surprised to see that the n integer sequence
(1,2,3,4,5,6...) doesn't appear first in all cases...
In spite of big number of result by using "|", perhaps the variation of this
number could give some sign...like the space between each integer inside one
sequence.


BestRegards
Eric