🚀 go-pugleaf

$BED>B$G$9!#(B

$B$b$&ITMW$@$H$O;W$$$^$9$,!"0l1~2rEz$r<($7$?$$$H;W$$$^$9!#(B

> $B!ZLdBj![(B  $B0lD>@~$KD9(B$B$$$9$4$m$/$,$"$j$^$9!#0l2s5Y$_$N#n%^%9<jA0$+$i=PH/(B
>	    $B$7$F%5%$%3%m$NL\$@$1$:$D?J$s$G$$$C$?$H$-!":G(B$B=*E*$K0l2s5Y$_$G(B
>	    $B$R$C$+$+$C$F$7$^$&3NN($r#p!J#n!K$H$7$^$9!#(B
>
>		  ------------------------       ----$B!|(B---
>		   |$B0l2s(B|    |    |    |   . . .   | $B"%(B |
>		   |$B5Y$_(B| $B#1(B | $B#2(B | $B#3(B |           | $B#n(B |
>		  ------------------------       ---------
>
>	   $B#1!%(B $B#p!J#n!K$,:GBg$H$J$k#n$H!"$=$N:GBgCM$r5a$a(B$B$F$/$@$5$$!#(B
>
>	   $B#2!%(B $B#n"*!g(B $B$H$7$?$H$-$N#p!J#n!K$N6K8B$r5a$a$F$/$@$5$$!#(B

$B$^$:!"(Bp(n) $B$NA22=<0$O(B

	6p(n)=p(n-1)+p(n-2)+p(n-3)+p(n-4)+p(n-5)+p(n-6)  (n>0)

$B$G!"=i4|>r7o$H$7$F(B p(0)=1, p(-1)=p(-2)= $B!D(B =0 $B$H$*$/$3$H$,$G$-$^$9!#(B

$B$=$3$G!"%$%a!<%8$,M/$/$h$&$K!"%0%i%U$r=q$$$F$_$^$9!#(B

 n    p(n)
 1  0.166667  *
 2  0.194444	       *
 3  0.226852			  *
 4  0.264660				      *
 5  0.308771						     *
 6  0.360232								      *
 7  0.253604				   *
 8  0.268094					*
 9  0.280369					    *
10  0.289288					       *
11  0.293393						*
12  0.290830					       *
13  0.279263					   *
14  0.283540					     *
15  0.286114					     *
16  0.287071					      *
17  0.286702					      *
18  0.285587					     *
19  0.284713					     *
20  0.285621					     *
21  0.285968					     *
22  0.285944					     *
23  0.285756					     *
24  0.285598					     *
25  0.285600					     *

$B$3$N$h$&$K!"(Bp(n) $B$OGH$rBG$A$J$,$i5^(B$BB.$K<}B+$7$F$$$/$o$1$G$9$,!"%0%i%U$+(B
$B$i$o$+$k$h$&$K!"(Bp(1),$B!D(B,p(5)<p(6) $B$H$J$j!"A22=<0$+$i(B p(n)<p(6) (n>6) $B$,(B
$B@.$jN)$D$3$H$,$o$+$k$N$G!"#1HV$NEz$($O(B p(6)=16807/46656 $B$H$J$j$^$9!#(B

$B$=$7$F!"#2HV$NJ}$G$9$,!"(B$BA22=<0$rJQ7A$9$k$H(B

	 6p(n)  +5p(n-1)+4p(n-2)+3p(n-3)+2p(n-4)+p(n-5)
	=6p(n-1)+5p(n-2)+4p(n-3)+3p(n-4)+2p(n-5)+p(n-6)

$B$H$J$k$3$H$+$i!"(Bn>=0 $B$K$*$$$F(B

	6p(n)+5p(n-1)+4p(n-2)+3p(n-3)+2p(n-4)+p(n-5)=6

$B$,@.(B$B$jN)$D$3$H$,$o$+$j$^$9!#$=$3$G!"(Bp(n)=q(n)+2/7 $B$H$*$/$H!"(B

	6q(n)+5q(n-1)+4q(n-2)+3q(n-3)+2q(n-4)+q(n-5)=0

$B$H$J$k$o$1$G$9$,!"$3$l$r$b$H$K(B q(n-1) $B$r>C5n$9$k$H(B

	36q(n)-q(n-2)-2q(n-3)-3q(n-4)-4q(n-5)-5q(n-6)=0

$B$H$J$k$3$H$+$i!"(B

	|q(n)|<=(|q(n-2)|+2|q(n-3)|+3|q(n-4)|+4|q(n-5)|+5|q(n-6)|)/36
	      <=(5/12)max{||q(n-2)|,$B!D(B,|q(n-6)|}

$B$h$j(B q(n)$B"*(B0 $B$H$J$j!"$3$l$+$i(B p(n)$B"*(B2/7 $B$,<($5$l$^$9!#(B

$B<B$O!"8e$G$h$/9M(B$B$($F$_$k$H!"(Bq(n-1) $B$r>C5n$9$k$H$$$&$N$O$^$C$?$/K\<AE*$G$O(B
$B$J$/!"EDJU;a$N$h$&$K(B

	42q(n)+5q(n-1)+3q(n-2)+q(n-3)-q(n-4)-3q(n-5)-5q(n-6)=0

$B$H$9$k$N$,:G$bI>2A$,NI$/$J$j$^$9!#(B

$B$3$N$h$&$K!"=iEyE*$J5DO@$@$1$G(B$B<}B+$r<($=$&$H$9$k$H>e$N$h$&$J%F%/%K%C%/$,(B
$BI,MW$K$J$k$o$1$G$9$,!"Dj?t78?t@~7A:9J,J}Dx<0$N0lHLO@$r;H$((B$B$P!"7hDjJ}Dx<0(B

	6z^6-z^5-z^4-z^3-z^2-z-1=(6z^5+5z^4+4z^3+3z^2+2z+1)(z-1)=0

$B$N(B z=1 $B0J30$N:,$N@dBPCM$,(B$B#1L$K~$G$"$k$3$H$r<($9$3$H$K$h$C$F!"(Bp(n) $B$N<}B+(B
$B$rJ]>Z$9$k$3$H$,$G$-$^$9!#$3$N$3$H$r<($9$K$O!"Nc$($PED(B$BJU;a$N$h$&$K(B

	(6z^5+5z^4+4z^3+3z^2+2z+1)(7z-5)=42z^6+5z^5+3z^4+z^3-z^2-3z-5

$B$HJQ7A$7$F(B Rouche $B$NDjM}(B$B$rE,MQ$7$F$b$$$$$N$G$9$,!"<!$N3]C+$NDjM}!J>ZL@$O(B
$B>JN,$7$^$9!K$rD>@\;H$&$3$H$K$h$C$F$b2DG=$G$9!#(B

$B!Z3](B$BC+$NDjM}![(B $B<B78?t$NJ}Dx<0(B a_0 z^n + a_1 z^(n-1) + $B!D(B + a_n = 0 $B$K$*(B
$B$$$F!"(Ba_0 > a_1 > $B!D(B > a_n > 0 $B$J(B$B$i$P!":,$N@dBPCM$O#1$h$j>.$5$$!#(B

$B$5$i$K!"(Bz=(5/6)z' $B$HCV$$$F3]C+$NDjM}$rE,MQ$9$k$3$H$K$h$C$F!":,$N@dBP(B$BCM$,(B
5/6 $BL$K~$G$"$k$3$H$,$o$+$k$N$G!"(Bp(n) $B$N<}B+$NB.$5$r6qBNE*$K(B

	p(n) = 2/7 + o((5/6)^n)

$B$HI>2A$9$k(B$B$3$H$b$G$-$^$9!#(B

$B$H$$$&$o$1$G!";d$NLdBj$KIU$-9g$C$F$$$m$$$m$HG:$s$G$/$@$5$C$?3'$5$s!"K\Ev(B
$B$K$"$j$,$H(B$B$&$4$6$$$^$7$?!#<B$O!"$3$NB>$K$b$$$/$D$+%l%/%j%(!<%7%g%sE*$JLd(B
$BBj$N%"%$%G%"$r;}$C$F$$$k$N$G!"$^$?5!2q(B$B$,$"$C$?$iN.$7$F$_$?$$$H;W$$$^$9!#(B


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	$BEl5~Bg3XBg3X1!(B $B?tM}2J3X8&5f2J(B $B?tM}2J3X@l96(B $B#M#1(B  $BED>B1Q<y(B
		E-mail: ss26022@ecc-s4.ecc.u-tokyo.ac.jp
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