A335206 a(n) is the total binary weight of all persolus bitstrings of length n.

1, 0, 2, 4, 5, 10, 18, 28, 46, 76, 121, 192, 305, 480, 751, 1172, 1822, 2822, 4359, 6716, 10322, 15830, 24230, 37020, 56467, 85998, 130787, 198640, 301325, 456568, 691050, 1044904, 1578457, 2382334, 3592594, 5413392, 8150894, 12264012, 18440269, 27709196

Offset

1,3

Comments

A bitstring is persolus if all of its 1's are isolated and each of its 0's possess at least one neighboring 0. The number of persolus bitstrings of length n is A179070(n+1).

Links

Table of n, a(n) for n=1..40.

Steven Finch, Variance of longest run duration in a random bitstring, arXiv:2005.12185 [math.CO], 2020.

Formula

G.f.: x*(1-x+x^2)^2/(1-x-x^3)^2.

Example

The only three persolus bitstrings of length 3 are 000, 100 and 001. The bitsums of these are 0, 1 and 1. Adding these give a(3)=2.
The only four persolus bitstrings of length 4 are 0000, 1000, 0001, and 1001. The bitsums of these are 0, 1, 1, and 2. Adding these give a(4)=4.
The only five persolus bitstrings of length 5 are 00000, 10000, 00100, 00001, and 10001. The bitsums of these are 0, 1, 1, 1 and 2. Adding these give a(5)=5.
The only eight persolus bitstrings of length 6 are 000000, 100000, 001000, 000100, 000001, 100100, 100001, and 001001. The bitsums of these are 0, 1, 1, 1, 1, 2, 2 and 2. Adding these give a(6)=10.

Crossrefs

Cf. A001629, A179070.

Sequence in context: A333188 A018401 A049332 * A096570 A046430 A133040

Adjacent sequences: A335203 A335204 A335205 * A335207 A335208 A335209

Keyword

nonn

Author

Steven Finch, May 26 2020

Status

approved