# [seqfan] Re: Large recurrences with small coefficients

Ron Hardin rhhardin at att.net
Wed Mar 23 19:40:51 CET 2011

```Some equivalent ones, but this time allowing 0 to be one of the numbers in the
sum

T(n,k)=Number of strictly increasing arrangements of n numbers in
-(n+k-2)..(n+k-2) with sum zero
https://oeis.org/A188181

Number of strictly increasing arrangements of 4 numbers in -(n+2)..(n+2) with
sum zero
Empirical: a(n)=3*a(n-1)-3*a(n-2)+2*a(n-3)-3*a(n-4)+3*a(n-5)-a(n-6)
https://oeis.org/A188182

Number of strictly increasing arrangements of 5 numbers in -(n+3)..(n+3) with
sum zero
Empirical: a(n)=2*a(n-1)-a(n-3)-2*a(n-5)+2*a(n-6)+a(n-8)-2*a(n-10)+a(n-11)
https://oeis.org/A188183

Number of strictly increasing arrangements of 6 numbers in -(n+4)..(n+4) with
sum zero
Empirical:
a(n)=3*a(n-1)-2*a(n-2)-a(n-3)+2*a(n-5)-a(n-6)-a(n-7)+2*a(n-8)-a(n-10)-2*a(n-11)+3*a(n-12)-a(n-13)

https://oeis.org/A188184

Number of strictly increasing arrangements of 7 numbers in -(n+5)..(n+5) with
sum zero
Empirical:
a(n)=2*a(n-1)-a(n-3)-a(n-5)+a(n-6)-2*a(n-7)+2*a(n-8)+a(n-9)-a(n-13)-2*a(n-14)+2*a(n-15)-a(n-16)+a(n-17)+a(n-19)-2*a(n-21)+a(n-22)

https://oeis.org/A188185

Number of strictly increasing arrangements of 8 numbers in -(n+6)..(n+6) with
sum zero
Empirical:
a(n)=3*a(n-1)-2*a(n-2)-3*a(n-4)+4*a(n-5)-3*a(n-8)+3*a(n-9)-a(n-11)-a(n-12)+3*a(n-14)-3*a(n-15)+4*a(n-18)-3*a(n-19)-2*a(n-21)+3*a(n-22)-a(n-23)

https://oeis.org/A188186

rhhardin at mindspring.com
rhhardin at att.net (either)

----- Original Message ----
> From: Ron Hardin <rhhardin at att.net>
> To: seqfan at list.seqfan.eu
> Sent: Mon, March 21, 2011 9:15:15 AM
> Subject: [seqfan] Large recurrences with small coefficients
>
> Some partition-related empirical linear recurrences that might factor
>
> https://oeis.org/A188123
> a(n)=2*a(n-1)-a(n-3)-a(n-4)+2*a(n-6)-a(n-7)
>
> https://oeis.org/A188124
> a(n)=2*a(n-1)-a(n-3)-2*a(n-5)+2*a(n-6)+a(n-8)-2*a(n-10)+a(n-11)
>
> https://oeis.org/A188125
> a(n)=2*a(n-1)-a(n-3)-a(n-5)+2*a(n-8)-a(n-11)-a(n-13)+2*a(n-15)-a(n-16)
>
> https://oeis.org/A188126
>a(n)=2*a(n-1)-a(n-3)-a(n-5)+a(n-6)-2*a(n-7)+2*a(n-8)+a(n-9)-a(n-13)-2*a(n-14)+2*a(n-15)-a(n-16)+a(n-17)+a(n-19)-2*a(n-21)+a(n-22)
>)
>
>
> https://oeis.org/A188127
>a(n)=2*a(n-1)-a(n-3)-a(n-5)+a(n-6)-a(n-7)+a(n-9)+a(n-10)+a(n-12)-2*a(n-13)-2*a(n-16)+a(n-17)+a(n-19)+a(n-20)-a(n-22)+a(n-23)-a(n-24)-a(n-26)+2*a(n-28)-a(n-29)
>)
>
>
> tabl https://oeis.org/A188122
> T(n,k)=Number of strictly increasing  arrangements of n nonzero numbers in
> -(n+k-2)..(n+k-2) with sum zero
>
>
>
> rhhardin at mindspring.com
> rhhardin at att.net (either)
>
>
> _______________________________________________
>
> Seqfan  Mailing list - http://list.seqfan.eu/
>

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