/sci/ - Science & Math

>>11193655
I don't think string theorists think of themselves as "out of the theoretical physics crew". When I think of a mathematical physicist then I think of the guys who study the theory of thermodynamics by framing it with notions such as lattice theory, or using the more fancy *-algebra spaces with this and that topology on it to really cast some classical electrodynamics potential questions on solid ground. Or studying the causal structure of spacetime in a way that looks less like Riemannian geometry but more like formal logic+topology.

>>11128599
Coding up

hasTwoBlacks[list_] := MemberQ[Table[list[[i]] + list[[i + 1]], {i, 1, Length@list - 1}], 2 b]
Table[Length@Select[Tuples[{w, b}, n], hasTwoBlacks], {n, 1, 15}]

in Mathematica returns
{0, 1, 3, 8, 19, 43, 94, 201, 423, 880, 1815, 3719, 7582, 15397, 31171}

and searching this on OEIS gives
https://oeis.org/A008466

>a(n) = 2^n - Fibonacci(n+2)

There are some references on the bottom of it, but none seem to spell it out nicely. I think the approach would be to create your formula by summing over all pairing positions (call it pivot pair) from left to right in the row, leaving the right of each pivot pair generic but restricting the left of each pivot pair to not have any pair.

>>11128563
He seemed sympathetic enough. I also need to lose weight again.