A333396 Total length of all longest runs of 0's in multus bitstrings of length n.

1, 2, 5, 11, 23, 45, 87, 165, 309, 573, 1056, 1934, 3527, 6408, 11605, 20960, 37771, 67928, 121949, 218595, 391302, 699610, 1249475, 2229329, 3974083, 7078658, 12599318, 22410548, 39837420, 70775727, 125675525, 223052519, 395702395, 701695820, 1243827018, 2204007329

Offset

1,2

Comments

A bitstring is multus if each of its 1's possess at least one neighboring 1.

The number of these bitstrings is A005251(n+2).

Links

Table of n, a(n) for n=1..36.

Steven Finch, Cantor-solus and Cantor-multus distributions, arXiv:2003.09458 [math.CO], 2020.

Formula

G.f.: x*Sum_{k>=1} (1+x^2)/(1-2*x+x^2-x^3)-(1+x^2-x^(k-1)+x^k-2*x^(k+1))/(1-2*x+x^2-x^3+x^(k+2)).

Example

a(4) = 11 because the seven multus bitstrings of length 4 are 0000, 1100, 0110, 0011, 1110, 0111, 1111 and the longest 0-runs contribute 4+2+1+2+1+1+0 = 11.

Crossrefs

Cf. A005251, A119706, A333394, A333395.

Sequence in context: A171985 A354044 A005986 * A277828 A147878 A179902

Adjacent sequences: A333393 A333394 A333395 * A333397 A333398 A333399

Keyword

nonn

Author

Steven Finch, Mar 18 2020

Status

approved