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 A067895 Write 2^n, 2^n+1, 2^n+2, ..., 2^(n+1)-1 in binary and add as if they were decimal numbers. 2
 1, 21, 422, 8444, 168888, 3377776, 67555552, 1351111104, 27022222208, 540444444416, 10808888888832, 216177777777664, 4323555555555328, 86471111111110656, 1729422222222221312, 34588444444444442624, 691768888888888885248, 13835377777777777770496, 276707555555555555540992 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 LINKS Table of n, a(n) for n=0..18. Index entries for linear recurrences with constant coefficients, signature (22,-40). FORMULA G.f.: (1 - x)/(1 - 22x + 40*x^2). a(n) = 2^(n-1)*(19*10^n - 1)/9. a(n) = 22*a(n-1) - 40*a(n-2). E.g.f.: exp(2*x)*(19*exp(18*x) - 1)/18. - Stefano Spezia, Apr 03 2023 EXAMPLE 2^2 to 2^3-1 = 4 through 7 = 100, 101, 110 and 111 in binary and when summed = 422. MATHEMATICA Table[Total[FromDigits[IntegerDigits[#, 2]]&/@(Range[2^n, 2^(n+1)-1])], {n, 0, 20}] Harvey P. Dale, May 20 2012 PROG (PARI) a(n)=if(n<0, 0, 2^(n-1)*(19*10^n-1)/9) CROSSREFS Cf. A067894. Sequence in context: A170740 A064108 A353144 * A215856 A297692 A218840 Adjacent sequences: A067892 A067893 A067894 * A067896 A067897 A067898 KEYWORD nonn,base,easy AUTHOR N. J. A. Sloane, May 15 2003 STATUS approved

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Last modified June 9 21:49 EDT 2023. Contains 363183 sequences. (Running on oeis4.)