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.

1, 4, 10, 21, 39, 64, 94, 129, 167, 212, 262, 317, 375, 440, 510, 585, 663, 748, 838, 933, 1031, 1136, 1246, 1361, 1479, 1604, 1734, 1869, 2007, 2152, 2302, 2457, 2615, 2780, 2950, 3125, 3303, 3488, 3678, 3873, 4071, 4276, 4486, 4701, 4919, 5144, 5374, 5609, 5847, 6092

Offset

1,2

Comments

Two decagons appearing at n >= 6. See illustration.

Links

Table of n, a(n) for n=1..50.

Kival Ngaokrajang, Illustration of initial terms

Formula

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

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

Prog

(PARI)
{
a=1; d1=0; p=a; print1(a, ", "); \\5s3b
for(n=2, 100,
   if(n<3, d1=2,
     if(n<4, d1=3,
       if(n<5, d1=5,
         if(n<6, d1=7,
           if(Mod(n, 4)==0, d1=5,
             if(Mod(n, 4)==1, d1=3,
               if(Mod(n, 4)==2, d1=7, d1=5
               )
             )
           )
         )
       )
     )
   );
   a=a+d1; p=p+a;
   print1(p, ", ")
)
}

Crossrefs

Cf. A253688 (vertex-to-vertex).

Sequence in context: A301213 A358042 A008121 * A253688 A049480 A216172

Adjacent sequences: A253684 A253685 A253686 * A253688 A253689 A253690

Keyword

nonn

Author

Kival Ngaokrajang, Jan 09 2015

Status

approved