[seqfan] Re: Denomination sequence

David Wilson davidwwilson at comcast.net
Sat Aug 15 09:00:33 CEST 2009


I don't find much time or motivation to submit these things lately. If you 
wish, please do.

----- Original Message ----- 
From: "Alois Heinz" <heinz at hs-heilbronn.de>
To: "Sequence Fanatics Discussion list" <seqfan at list.seqfan.eu>
Sent: Friday, August 14, 2009 2:33 PM
Subject: [seqfan] Re: Denomination sequence


> Nice sequence.  Do you need a program or more?
>
> b:= proc(n,i) option remember;
>   if n<0 then 0
> elif n=0 then 1
> elif i<0 then 0
> elif i=1 then n+1
> else b(n,i-1) +b(n-a(i),i)
>   fi
> end:
> a:= n-> b(n,n-1):
> seq (a(n), n=0..100);
>
> 1, 1, 3, 5, 7, 10, 14, 19, 25, 32, 42, 53, 66, 82, 101, 124, 150, 181,
> 216, 257,
> 306, 361, 424, 495, 577, 671, 776, 895, 1029, 1180, 1350, 1540, 1752, 
> 1988,
> 2252, 2547, 2872, 3231, 3630, 4071, 4558, 5093, 5683, 6330, 7040, 7822,
> 8674,
> 9606, 10625, 11738, 12952, 14270, 15708, 17270, 18966, 20808, 22803, 
> 24965,
> 27303, 29835, 32571, 35521, 38707, 42143, 45845, 49829, 54117, 58730,
> 63683,
> 69004, 74718, 80842, 87408, 94445, 101979, 110040, 118661, 127882, 137730,
> 148244, 159472, 171447, 184217, 197826, 212327, 227768, 244197, 261683,
> 280274,
> 300033, 321030, 343331, 367009, 392127, 418779, 447044, 476997, 508739,
> 542360,
> 577958, 615633
>
> Alois
>
> David Wilson schrieb:
>> 1 1 3 5 7 10 14 19 25 32 42 53 66 82 101 124 150 181 216 257 306
>>
>> Start at the 0th coin. The value of the nth coin is the number of ways
>> to make change for n cents in earlier coins. The two penny coins are
>> considered distinct.
>>
>> g.f: g(x) = PROD(n >= 0; 1/(1-x^a(n))) - x
>>
>>
>> _______________________________________________
>>
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>>
>>
>
>
>
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>
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