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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

Table of n, a(n) for n=1..42.

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.)