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 A262699 List of currency denominations such that any value x > 0 is represented in exactly x ways as a sum of distinct denominations, where a repeated value represents a bill and a coin which count as distinct denominations. 0
 1, 2, 2, 3, 4, 4, 8, 8, 16, 16, 32, 32, 64, 64, 128, 128, 256, 256, 512, 512, 1024, 1024, 2048, 2048, 4096, 4096, 8192, 8192, 16384, 16384, 32768, 32768, 65536, 65536, 131072, 131072, 262144, 262144, 524288, 524288, 1048576, 1048576 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 LINKS David Wilson, Currency puzzle, SeqFan list, Sept. 25, 2015. Index entries for linear recurrences with constant coefficients, signature (0,2). FORMULA a(n) = 2^ceiling(n/2-1) for n>4. G.f.: x*(1 - x)*(1 + 3*x + 3*x^2 + 2*x^3 + 2*x^4)/(1 - 2*x^2). [Bruno Berselli, Sep 28 2015] PROG (PARI) a(n)=2^((n-1)\2)+if(n<5, !bittest(n, 0)) (MAGMA)  [n le 4 select Floor(n/2+1) else 2^Ceiling(n/2-1): n in [1..45]]; // Vincenzo Librandi, Sep 28 2015 CROSSREFS Sequence in context: A036813 A036814 A137776 * A153946 A036810 A036809 Adjacent sequences:  A262696 A262697 A262698 * A262700 A262701 A262702 KEYWORD nonn,easy AUTHOR M. F. Hasler, Sep 27 2015 STATUS approved

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Last modified August 20 08:50 EDT 2018. Contains 313914 sequences. (Running on oeis4.)