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
KEYWORD
nonn,easy
AUTHOR
N. J. A. Sloane, Jul 11 2015
EXTENSIONS
Edited by Reinhard Zumkeller, Jul 13 2015
STATUS
approved