[seqfan] Re: Currency puzzle

[Rob Pratt]

If a coin and a bill of the same value cannot be used simultaneously, I get the following.

G.F.: (1+x)(1+2x^2)(1+x^3)(1+2x^4)(1+2x^8)(1+2x^16)(1+2x^32)(1+2x^64)

seq: 1, 1, 2, 3, 3, 4, 6, 6, 4, 6, 8, 6, 6, 8, 12, 12, 6, 10, 12, 6, 6, 8, 12, 12, 8, 12, 16, 12, 12, 16, 24, 24, 10, 18, 20, 6, 6, 8, 12, 12, 8, 12, 16, 12, 12, 16, 24, 24, 12, 20, 24, 12, 12, 16, 24, 24, 16, 24, 32, 24, 24, 32, 48, 48, 18, 34, 36, 6, 6, 8, 12, 12, 8, 12, 16, 12, 12, 16, 24, 24, 12, 20, 24, 12, 12, 16, 24, 24, 16, 24, 32, 24, 24, 32, 48, 48, 20, 36, 40, 12, 12, 16, 24, 24, 16, 24, 32, 24, 24, 32, 48, 48, 24, 40, 48, 24, 24, 32, 48, 48, 32, 48, 64, 48, 48, 64, 96, 96, 32, 64, 64

-----Original Message-----
From: SeqFan [mailto:seqfan-bounces at list.seqfan.eu] On Behalf Of David Wilson
Sent: Thursday, September 24, 2015 9:10 PM
To: 'Sequence Fanatics Discussion list' <seqfan at list.seqfan.eu>
Subject: [seqfan] Currency puzzle

Frobenia has a currency based on the blatz, in the following denominations:

 

1, 2, 2, 3, 4, 4, 8, 8, 16, 16, 32, 32, 64, 64, .

 

A value listed once is available only as a coin.

A value listed twice as a coin and a bill, counted as distinct denominations.

How many ways are there to make change for N blatz using distinct denominations?


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