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User:Anton Zakharov

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I have a degree in economics and reside in Moscow. Besides stock market my interests lie in the field of combinatorics.

Here is a curious method of generating many sequences from matrices: https://oeis.org/w/images/e/e3/Anton_Zakharov%2C_Matrix-related_sequences_.pdf

Mandatory courses in linear algebra or operations research never were my forte at the university so it is a rather unexpected consequence of my studies.

Namely, A001711, A001705 (generalized Stirling numbers), A000124 (the Lazy Caterer's sequence), A182541 and probably many others as well can be obtained with the help of the exact same procedure of deletion of elements from matrices and counting the number of elements left. In fact, it still remains an open problem (at least for me) to determine whether a —Āertain sequence can be obtained by the means of this method or not. What is the necessary condition?


Various formulas counting the number of permutations:

A030297(n)+ A002104(n) = A007526(n) + A006231(n+1).

A001711(n) = A001705(n+2) - A182541(n+4).

A000522(n) = A038155(n+2)/A000217(n+1).

A052801(n) = A007840(n) + A215916(n)

A067318(n) + A001705(n-1) = A062119(n)

Several of them have been found empirically from this useful configuration:

http://imageshack.com/a/img924/259/i36XVh.jpg

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