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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
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Table of n, a(n) for n=0..31.

Steven Finch, Cantor-solus and Cantor-multus 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*x-4*x^2-3*x^3+x^4)/(-1+2*x-x^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 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.

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.

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

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Last modified May 9 13:42 EDT 2021. Contains 343742 sequences. (Running on oeis4.)