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 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

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