User:William P. Orrick

I work in mathematical physics and combinatorics. I have contributed to a number of sequences relating to (0,1) matrices, Hadamard matrices, and combinatorial designs.

Recently (as of March 2023) I have been adding sequences related to the continued fraction of e and to the dice problem described at A273013 and A131514.

To-do list. (If anyone seeing this wants to take any of these on, feel free.)

• A131514 - add cross ref. to A360098, and to A360439, A360440, if approved.
• A273013 - add cross refs. to A360439, A360440, if approved.
• A360098 - add bfile; add cross refs. to A360439, A360440, if approved.
• A168422 - formula seems to need correction: "T(n,k) = " is repeated; lower bound in summation should be k, not 0; add program and bfile; add cross ref. to A360441, if approved. (All but cross ref. to A360441 proposed for review 24 March 2023. Also an extraneous term 0 removed from sequence and some additional cross refs. added. Added: changes approved 31 March 2023. Can now add cross ref. to A360441 since it was approved as well.)
• A253667 - add bfile, additional program; add cross ref. to A360441, if approved, and maybe also to A168422. Maybe also create new companion sequence whose terms are the triangle elements multiplied by C(n,k). This new triangle relates more directly to A360441 and has a very nice Pascal's-triangle-like recurrence. The inverse of this new triangle, interpreted as an infinite matrix, is also interesting and could be added. The k = 0 column, starting with the n = 1 row, is -|A002119|, while the the row sums of all rows starting with n = 1 are 0 with all elements in columns k > 0 apparently positive, and possibly combinatorially meaningful.
• A360439 and A360440 should cross reference each other, if both are approved. Also, bfiles should be added to both.