# Generalising Unique Sums

Michael Somos somos at grail.cba.csuohio.edu
Tue Jan 11 20:15:55 CET 2000

```Wouter Meeussen wrote :

> the next column isn't:
> {4,12,32,55,108,154,256,333,500,616,864,1027,1372,1590,2048,2329,...}

True, the EIS can't contain *every* sequence imaginable. However, ...

gp> print(Vec(O(x^20)+(2+x+x^2)/((1-x)*(1-x^2))))
[2, 3, 6, 7, 10, 11, 14, 15, 18, 19, 22, 23, 26, 27, 30, 31, 34, 35, 38, 39]

%S A042964 2,3,6,7,10,11,14,15,18,19,22,23,26,27,30,31,34,35,38,39,
%N A042964 Congruent to 2 or 3 mod 4.

gp> print(Vec(O(x^20)+(1+x+2*x^3)/((1-x)*(1-x^2))))
[1, 2, 3, 6, 7, 10, 11, 14, 15, 18, 19, 22, 23, 26, 27, 30, 31, 34, 35, 38]

gp> print(Vec(O(x^19)+(1+x+2*x^3)/((1-x)*(1-x^2)^2)))
[1, 2, 4, 8, 11, 18, 22, 32, 37, 50, 56, 72, 79, 98, 106, 128, 137, 162, 172]

gp> print(Vec(O(x^16)+deriv(x*(1+x+2*x^3)/((1-x)*(1-x^2)^2))))
[1, 4, 12, 32, 55, 108, 154, 256, 333, 500, 616, 864, 1027, 1372, 1590, 2048]

Shalom, Michael

--
Michael Somos <somos at grail.cba.csuohio.edu>     Cleveland State University
http://grail.cba.csuohio.edu/~somos/            Cleveland, Ohio, USA 44115

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