|
%I #7 Jan 15 2015 12:38:26
%S 1,4,10,21,39,64,94,129,167,212,262,317,375,440,510,585,663,748,838,
%T 933,1031,1136,1246,1361,1479,1604,1734,1869,2007,2152,2302,2457,2615,
%U 2780,2950,3125,3303,3488,3678,3873,4071,4276,4486,4701,4919,5144,5374,5609,5847,6092
%N The total number of pentagons in a variant of pentagon expansion (side-to-side, two consecutive sides and one isolated side) after n iterations.
%C Two decagons appearing at n >= 6. See illustration.
%H Kival Ngaokrajang, <a href="/A253687/a253687.pdf">Illustration of initial terms</a>
%F Conjecture: a(n) = 2*a(n-1)-a(n-2)+a(n-4)-2*a(n-5)+a(n-6) for n>7. - _Colin Barker_, Jan 09 2015
%F Empirical g.f.: x*(4*x^8-2*x^6-5*x^5-6*x^4-5*x^3-3*x^2-2*x-1) / ((x-1)^3*(x+1)*(x^2+1)). - _Colin Barker_, Jan 09 2015
%o (PARI)
%o {
%o a=1;d1=0;p=a;print1(a,", ");\\5s3b
%o for(n=2,100,
%o if(n<3,d1=2,
%o if(n<4,d1=3,
%o if(n<5,d1=5,
%o if(n<6,d1=7,
%o if(Mod(n,4)==0,d1=5,
%o if(Mod(n,4)==1,d1=3,
%o if(Mod(n,4)==2,d1=7,d1=5
%o )
%o )
%o )
%o )
%o )
%o )
%o );
%o a=a+d1;p=p+a;
%o print1(p,", ")
%o )
%o }
%Y Cf. A253688 (vertex-to-vertex).
%K nonn
%O 1,2
%A _Kival Ngaokrajang_, Jan 09 2015
|
