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

Author

Steven Finch, Mar 18 2020

Keywords

• nonn

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).

Examples

			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.
		

Links

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

Crossrefs

Cf. A005251, A119706, A333394, A333395.

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)).