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A332863 Total binary weight squared of all A005251(n) binary sequences of length n not containing any isolated 1's. 1

%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">Cantor-solus and Cantor-multus 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*x-4*x^2-3*x^3+x^4)/(-1+2*x-x^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 2-bitstrings 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 3-bitstrings 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

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Last modified June 20 09:13 EDT 2021. Contains 345162 sequences. (Running on oeis4.)