A256429 a(n) is the total number of pentagrams in a variant of pentagram fractal after n iterations.

1, 6, 11, 16, 41, 106, 211, 416, 941, 2106, 4411, 9316, 20341, 44106, 94111, 201716, 435741, 938606, 2014311, 4330116, 9324641, 20060606, 43122511, 92747016, 199552041, 429222606, 923076211, 1985467416, 4270895441, 9186237106, 19758020411, 42498043816, 91411232341

Offset

0,2

Comments

Inspired by A255870. But at the higher iterations, the perimeter would be a pentagram instead of a pentagon. See illustration in the links.

Links

Table of n, a(n) for n=0..32.

Kival Ngaokrajang, Illustration of initial terms, Illustration of n = 6

Formula

Conjectures from Colin Barker, Mar 29 2015: (Start)

a(n) = 3*a(n-1)-4*a(n-2)+7*a(n-3)-5*a(n-4) for n>3.

G.f.: -(3*x^2-3*x-1) / ((x-1)*(5*x^3-2*x^2+2*x-1)).

(End)

Prog

(Small Basic)
a[1]=1
a[2]=0
a[3]=0
a[4]=4
TextWindow.Write("1, 6, 11, 16, 41, ")
b=0
s=41
rs=5
For n=5 To 50
  b=b+a[n-4]
  a[n]=4*(2*b+3*(a[n-3]/4))
  rs=rs+a[n]
  s=s+5*rs
  TextWindow.Write(s+", ")
EndFor

Crossrefs

Cf. A255870.

Sequence in context: A208719 A208775 A242916 * A024730 A024952 A278833

Adjacent sequences: A256426 A256427 A256428 * A256430 A256431 A256432

Keyword

nonn

Author

Kival Ngaokrajang, Mar 28 2015

Status

approved