login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A259966 Total binary weight (cf. A000120) of all A005251(n) binary sequences of length n not containing any isolated 1's. 3
0, 0, 2, 7, 16, 34, 72, 149, 300, 593, 1158, 2239, 4292, 8168, 15450, 29072, 54456, 101597, 188878, 350038, 646880, 1192415, 2192956, 4024583, 7371884, 13479421, 24607048, 44853552, 81645236, 148424000, 269497614, 488784787, 885571340, 1602879242, 2898512344 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

REFERENCES

R. K. Guy, Letter to N. J. A. Sloane, Feb 05 1986.

LINKS

Reinhard Zumkeller, Table of n, a(n) for n = 0..1000

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

R. K. Guy, Letter to N. J. A. Sloane, Feb 1986

Index entries for linear recurrences with constant coefficients, signature (4,-6,6,-5,2,-1).

FORMULA

a(n) = a(n-1)+a(n-2)+2*b(n)+a(n-4)+3*b(n-2), where b() is A005251().

G.f.: -x^2*(x-2) / (x^3-x^2+2*x-1)^2. - Colin Barker, Jul 21 2015

a(n) = Sum_{k=1..n} k * 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 of these are 0 and 2.  Adding these give a(2)=2.

The only four 3-bitstrings without isolated 1's are 000, 011, 110 and 111.  The bitsums of these are 0, 2, 2 and 3.  Adding these give a(3)=7.

PROG

(Haskell)

a259966 n = a259966_list !! n

a259966_list = 0 : 0 : 2 : 7 : zipWith (+)

   (zipWith3 (((+) .) . (+))

             a259966_list (drop 2 a259966_list) (drop 3 a259966_list))

   (drop 2 $ zipWith (+)

             (map (* 2) $ drop 2 a005251_list) (map (* 3) a005251_list))

-- Reinhard Zumkeller, Jul 13 2015

(PARI) concat([0, 0], Vec(-x^2*(x-2)/(x^3-x^2+2*x-1)^2 + O(x^50))) \\ Colin Barker, Jul 21 2015

CROSSREFS

Cf. A005251, A097230.

Sequence in context: A023612 A192952 A132738 * A283500 A097442 A345025

Adjacent sequences:  A259963 A259964 A259965 * A259967 A259968 A259969

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane, Jul 11 2015

EXTENSIONS

Edited by Reinhard Zumkeller, Jul 13 2015

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified June 18 11:39 EDT 2021. Contains 345098 sequences. (Running on oeis4.)