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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. 5
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 (list; graph; refs; listen; history; text; internal format)
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: A009898 A301213 A008121 * A253688 A049480 A216172

Adjacent sequences:  A253684 A253685 A253686 * A253688 A253689 A253690

KEYWORD

nonn

AUTHOR

Kival Ngaokrajang, Jan 09 2015

STATUS

approved

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Last modified October 15 09:26 EDT 2018. Contains 316211 sequences. (Running on oeis4.)