%I
%S 0,0,4,17,46,116,288,683,1548,3403,7320,15461,32146,65954,133800,
%T 268804,535434,1058533,2078732,4057858,7878814,15223495,29285368,
%U 56109673,107108104,203766859,386443052,730768044,1378180568,2592664120,4866008208,9112796113
%N Total binary weight squared of all A005251(n) binary sequences of length n not containing any isolated 1's.
%H Steven Finch, <a href="https://arxiv.org/abs/2003.09458">Cantorsolus and Cantormultus distributions</a>, arXiv:2003.09458 [math.CO], 2020.
%H <a href="/index/Rec#order_09">Index entries for linear recurrences with constant coefficients</a>, signature (6,15,23,27,24,16,9,3,1).
%F G.f.: x^2*(4+7*x4*x^23*x^3+x^4)/(1+2*xx^2+x^3)^3.
%F a(n) = Sum_{k=1..n} k^2 * A097230(n,k).  _Alois P. Heinz_, Mar 03 2020
%e The only two 2bitstrings without isolated 1's are 00 and 11. The bitsums squared of these are 0 and 4. Adding these give a(2)=4.
%e The only four 3bitstrings without isolated 1's are 000, 011, 110 and 111. The bitsums squared of these are 0, 4, 4 and 9. Adding these give a(3)=17.
%Y Cf. A005251, A097230, A259966.
%K nonn,easy
%O 0,3
%A _Steven Finch_, Feb 27 2020
