[seqfan] Re: Long Linear Recurrences with Small Coefficients

Joerg Arndt arndt at jjj.de
Fri Jan 14 16:51:25 CET 2011

```* Ron Hardin <rhhardin at att.net> [Jan 14. 2011 15:58]:
> I meant to point out some long recurrences with mostly +-1 coefficients, and ask
> if it implied anything
>
> http://oeis.org/A183913

\r ser2prod.gpi
a(n)=x^n
t=-a(0)+a(1)+2*a(2)-a(3)-a(4)-a(5)+a(9)-a(10)+3*a(12)+a(13)-a(14)-a(16)-2*a(17)-a(18)-a(20)+a(22)+2*a(23)+2*a(24)+a(25)-a(27)-a(29)-2*a(30)-a(31)-a(33)+a(34)+3*a(35)-a(37)+a(38)-a(42)-a(43)-a(44)+2*a(45)+a(46)-a(47)
t=Vec(t)
printprod(ser2prod(t))
1 * (1-y^1)^{1} * (1-y^2)^{2} * (1-y^3)^{1} * (1-y^4)^{1} * (1-y^5)^{1} * (1-y^6)^{1} * (1-y^7)^{1} * (1-y^8)^{1} * (1-y^9)^{1}

( in all following exponents of +1 will be suppressed, first repeat the above: )
1 * (1-y^1) * (1-y^2)^{2} * (1-y^3) * (1-y^4) * (1-y^5) * (1-y^6) * (1-y^7) * (1-y^8) * (1-y^9)

This looks partition-ish (note 9 vs. -5...+5, but note exponent with 1-y^2)

> http://oeis.org/A183929

1 * (1-y^1)^{2} * (1-y^5)^{-1} * (1-y^8) * (1-y^9) * (1-y^10) * (1-y^15) * (1-y^24)

> http://oeis.org/A183921

1 * (1-y^1)^{2} * (1-y^5)^{-1} * (1-y^8) * (1-y^9) * (1-y^10) * (1-y^15) * (1-y^24)

Same as A183929!

>
> and some neighbors with A-numbers differing by small constants.
>

http://oeis.org/A183914

1 * (1-y^1) * (1-y^2)^{2} * (1-y^3) * (1-y^4) * (1-y^5)^{2} * (1-y^6) * (1-y^7) * (1-y^8) * (1-y^9) * (1-y^11)
(note 11 vs, -6...+6, but also exponents at 1-y^2 and 1-y^5)

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