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A256429
a(n) is the total number of pentagrams in a variant of pentagram fractal after n iterations.
8
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.
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
KEYWORD
nonn
AUTHOR
Kival Ngaokrajang, Mar 28 2015
STATUS
approved