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User:Danny Rorabaugh

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Danny Rorabaugh is a postdoctoral fellow at Queen's University Sep 2015 -- Dec 2017 and at the University of Delaware starting Jan 2018.

Words

My dissertation at the University of South Carolina was Toward the Combinatorial Limit Theory of Free Words.

The sequences most relevant to that words research involve...

... Zimin words: A082215 (see Kamenetsky's formula) and A123121 (but actually A000225);

... words with(out) a palindrome/square/bifix: A003000(A094536), A019308(A094538), A248122(A252696), A249629(A252697), and A249638(A252698) thru A249643(A252703);

... word structures: A000110, A056272-A056273, A164863-A164864, A203641, A255706 (my favorite submission).

Puzzles

Here are a few puzzle sequences I've created that are not in the OEIS (at the time of posting). Please message me if you've figured out a pattern.

[2015-04] 1,1,1,1,2,1,2,1,5,3,2,2,2,1,2,2,1,1,5,2,1,2,1,1,15,...

[2017-09] 1,2,3,5,11,37,277,4907,...

[2017-09] 5,4,3,4,7,5,3,4,4,5,4,6,6,9,11,9,...

[2017-09] 2,3,5,7,9,11,15,16,17,19,21,22,...

[2017-09] 1,4,6,10,12,18,22,28,32,42,46,58,...

Tables

I don't care much for sequences that are tables, but I do like a good table of sequences.

Cecilia Rossiter posted several sequences (most of A101089-A101104) involving the function MagicNKZ(n,k,z) = Sum_{j=0..k+1} (-1)^j*binomial(n+1-z,j)*(k-j+1)^n, for which I made the following table. Please email me if you find any inaccurate cross-references (other than shifted offset) or sequences that fill the holes.

Note: filling in holes in a table like this is NOT sufficient reason to submit a new sequence!

...... |  n = 1  |  n = 2  |  n = 3  |  n = 4  |  n = 5  |  n = 6  |  n = 7  |  n = 8 
--------------------------------------------------------------------------------------
z =  0 | A000007 | A019590 | .......  MagicNKZ(n,k,0) = T(n,k+1) from A008292  .......
z =  1 | A000012 | A040000 | A101101 | A101104 | A101100 | ....... | ....... | .......
z =  2 | A000027 | A005408 | A008458 | A101103 | A101095 | ....... | ....... | ....... 
z =  3 | A000217 | A000290 | A003215 | A005914 | A101096 | ....... | ....... | ....... 
z =  4 | A000292 | A000330 | A000578 | A005917 | A101098 | ....... | ....... | ....... 
z =  5 | A000332 | A002415 | A000537 | A000583 | A022521 | ....... | A255181 | ....... 
z =  6 | A000389 | A005585 | A024166 | A000538 | A000584 | A022522 | A255177 | A255182 
z =  7 | A000579 | A040977 | A101094 | A101089 | A000539 | A001014 | A022523 | A255178 
z =  8 | A000580 | A050486 | A101097 | A101090 | A101092 | A000540 | A001015 | A022524 
z =  9 | A000581 | A053347 | A101102 | A101091 | A101099 | A101093 | A000541 | A001016 
z = 10 | A000582 | A054333 | A254469 | A254681 | A254644 | A254640 | A250212 | A000542 
z = 11 | A001287 | A054334 | A254869 | A254470 | A254682 | A254645 | A254641 | A253636 
z = 12 | A001288 | A057788 | ....... | A254870 | A254471 | A254683 | A254646 | A254642 
z = 13 | A010965 | ....... | ....... | ....... | A254871 | A254472 | A254684 | A254647 
z = 14 | A010966 | ....... | ....... | ....... | ....... | A254872 | ....... | .......