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 A166079 Given a row of n payphones, all initially unused, how many people can use the payphones, assuming (1) each always chooses one of the most distant payphones from those in use already, (2) the first person takes a phone at the end, and (3) no people use adjacent phones? 2
 1, 1, 2, 2, 3, 3, 3, 4, 5, 5, 5, 5, 5, 6, 7, 8, 9, 9, 9, 9, 9, 9, 9, 9, 9, 10, 11, 12, 13, 14, 15, 16, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 33, 33, 33, 33, 33, 33, 33, 33, 33, 33, 33, 33, 33 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 LINKS Table of n, a(n) for n=1..78. H.-K. Hwang, S. Janson, and T.-H. Tsai. Exact and asymptotic solutions of the recurrence f(n) = f(floor(n/2)) + f(ceiling(n/2)) + g(n): theory and applications. Preprint, 2016. H.-K. Hwang, S. Janson, and T.-H. Tsai. Exact and Asymptotic Solutions of a Divide-and-Conquer Recurrence Dividing at Half: Theory and Applications. ACM Transactions on Algorithms, 13:4 (2017), #47. DOI:10.1145/3127585 Randall Munroe, Urinal protocol vulnerability Simon Wundling, About a combinatorial problem with n seats and n people, arXiv:2303.18175 [math.CO], 2023. (German) FORMULA a(n) = 1 + 2^floor(log_2(n-2) - 1) + max(0, n - (3/2) * 2^floor(log_2(n-2)) - 1). A recurrence is: a(n) = a(m) + a(n-m+1) - 1, with a(1) = a(2) = 1 and a(3)=2, where m = ceiling(n/2). - John W. Layman, Feb 05 2011 a(n) = n - b(n,1) (See A095236 for definition and calculation of b(n,1)). - Simon Wundling, May 21 2023 PROG (PARI) A000523(n)=my(t=floor(sizedigit(n)*3.32192809)-5); n>>=t; while(n>3, n>>=2; t+=2); if(n==1, t, t+1); a(n)=my(t=1<<(A000523(n-2)-1)); max(t+1, n-t-t) (PARI) a(n) = if(n<3, return(1)); my(L=logint(n-2, 2)-1); 1 + 2^L + max(0, n - 3*2^L - 1) \\ Charles R Greathouse IV, Jan 27 2016 CROSSREFS Cf. A095236, A095912, A095240. Sequence in context: A334922 A301851 A101646 * A269381 A080677 A344497 Adjacent sequences: A166076 A166077 A166078 * A166080 A166081 A166082 KEYWORD easy,nonn AUTHOR Charles R Greathouse IV, Oct 06 2009 STATUS approved

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Last modified November 30 23:17 EST 2023. Contains 367463 sequences. (Running on oeis4.)