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A253687 The total number of pentagons in a variant of pentagon expansion (side-to-side, two consecutive sides and one isolated side) after n iterations.

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