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A253688
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The total number of pentagons in a variant of pentagon expansion (vertex-to-vertex, two consecutive vertices and one isolated vertex) after n iterations.
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6
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1, 4, 10, 21, 39, 64, 94, 129, 171, 218, 272, 331, 397, 468, 546, 629, 719, 814, 916, 1023, 1137, 1256, 1382, 1513, 1651, 1794, 1944, 2099, 2261, 2428, 2602, 2781, 2967, 3158, 3356, 3559, 3769, 3984, 4206, 4433, 4667, 4906, 5152, 5403, 5661, 5924, 6194, 6469, 6751, 7038
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refs;
listen;
history;
text;
internal format)
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OFFSET
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1,2
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COMMENTS
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Two star shaped icosagons appearing at n >= 6. See illustration.
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LINKS
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FORMULA
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a(n) = (53-(-1)^n-38*n+12*n^2)/4 for n>5.
a(n) = 2*a(n-1)-2*a(n-3)+a(n-4) for n>9.
G.f.: -x*(2*x^8-2*x^7-2*x^6+2*x^5+4*x^4+3*x^3+2*x^2+2*x+1) / ((x-1)^3*(x+1)).
(End)
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PROG
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(PARI)
{
a=1; d1=0; p=a; print1(a, ", "); \\5v3b
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(n<7, d1=7,
if(n<8, d1=5,
if(Mod(n, 2)==0, d1=5, d1=7
)
)
)
)
)
)
);
a=a+d1; p=p+a;
print1(p, ", ")
)
}
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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