[seqfan] Re: A092236 Maths Olympiad problem

[Kevin Ryde]

mt.kongtong at gmail.com (Tw Mike) writes:
>
> You could download the book online.

I saw a little for free at Springer, but not that page ... :)

primeness at borve.org (Neil Fernandez) writes:
>
> The question was proposed at the IMO in 1992 and got on to the long
> list, as q19, but not the shortlist.

Thanks.  (Its strip factors of 3 is the terdragon turn sequence, sum net
direction, then divisible by 3 is count segments in initial direction.)

Another I found in case its of interest, with x=1 y=2 a=0 m=3 giving
A092236 I think (and friends A135254 A133474 for a=1 and a=2).

  Benjamin Justus, "Extension of Ramus' Identity with Applications",
  Siauliai Mathematical Seminar, 8 (16), 2013, pages 109-115.
  http://siauliaims.su.lt/index.php?option=com_content&view=article&id=338&Itemid=7
  http://siauliaims.su.lt/pdfai/2013/Just-2013.pdf

Pari:
S(x,y,a,m,k) = sum(l=0,k, my n; n=l*m+a; binomial(k,n)*x^n*y^(k-n));
x=1; y=2; m=3;
a=0; vector(20,k, S(x,y,a,m,k-1))
a=1; vector(20,k, S(x,y,a,m,k-1))
a=2; vector(20,k, S(x,y,a,m,k-1))