

A332863


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


1



0, 0, 4, 17, 46, 116, 288, 683, 1548, 3403, 7320, 15461, 32146, 65954, 133800, 268804, 535434, 1058533, 2078732, 4057858, 7878814, 15223495, 29285368, 56109673, 107108104, 203766859, 386443052, 730768044, 1378180568, 2592664120, 4866008208, 9112796113
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OFFSET

0,3


LINKS

Table of n, a(n) for n=0..31.
Steven Finch, Cantorsolus and Cantormultus distributions, arXiv:2003.09458 [math.CO], 2020.
Index entries for linear recurrences with constant coefficients, signature (6,15,23,27,24,16,9,3,1).


FORMULA

G.f.: x^2*(4+7*x4*x^23*x^3+x^4)/(1+2*xx^2+x^3)^3.
a(n) = Sum_{k=1..n} k^2 * A097230(n,k).  Alois P. Heinz, Mar 03 2020


EXAMPLE

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.
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.


CROSSREFS

Cf. A005251, A097230, A259966.
Sequence in context: A147656 A095667 A212577 * A119949 A213499 A213502
Adjacent sequences: A332860 A332861 A332862 * A332864 A332865 A332866


KEYWORD

nonn,easy


AUTHOR

Steven Finch, Feb 27 2020


STATUS

approved



