■排他的数列(その9)
うまく一意に定まらないので,答えから逆にたどることにした.
{an}={1,4,6,7,10,11,13,16}
{bn}={2,3,5,8,9,12,14,15}
===================================
{an}={1,3,5,7,9,11,13,15}
{bn}={2,4,6,8,10,12,14,16}
{an^2}={1,9,25,49,81,121,169,225}
{bn^2}={4,16,36,64,100,144,196,256}
{cn}={bn^2−an^2}={3,−7,−11,15,−19,23,27,−31}=0
{an^3}={1,27,125,343,729,1331,2197,3375}}
{bn^3}={8,64,216,512,1000,1728,2744,4096}
{dn}={cn+1−cn}={30,−54,−78,102,−126,150,−174}=0
{cn}={bn^3−an^3}={7,−37,−91,169,−271,397,547,−721}=0
4個ずつ{}するとき,両端の2項あるいは中央の2項が符号が変わるのだろうか?
===================================