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A253547
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The total number of star-shaped dodecagons appearing in a variant of hexagon expansion after n iterations.
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4
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0, 0, 0, 1, 3, 9, 16, 23, 33, 43, 56, 69, 85, 101, 120, 139, 161, 183, 208, 233, 261, 289, 320, 351, 385, 419, 456, 493, 533, 573, 616, 659, 705, 751, 800, 849, 901, 953, 1008, 1063, 1121, 1179, 1240, 1301, 1365, 1429, 1496, 1563, 1633, 1703, 1776, 1849, 1925, 2001, 2080
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listen;
history;
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internal format)
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OFFSET
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1,5
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COMMENTS
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Total number of hexagons after n iterations is A179178. See illustration.
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LINKS
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FORMULA
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a(n) = (27 - 3*(-1)^n - 28*n + 6*n^2)/8 for n>5.
a(n) = 2*a(n-1) - 2*a(n-3) + a(n-4) for n>6.
G.f.: -x^4*(2*x^5 - 4*x^4 + 3*x^2 + x + 1) / ((x-1)^3*(x+1)).
(End)
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MATHEMATICA
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LinearRecurrence[{2, 0, -2, 1}, {0, 0, 0, 1, 3, 9, 16, 23, 33}, 60] (* Harvey P. Dale, Oct 30 2015 *)
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PROG
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(PARI)
{
a=1; d1=0; print1("0, 0, 0, 1", ", ");
for(n=4, 100,
if(n<5, d1=2,
if(n<6, d1=6,
if(n<7, d1=7,
if(Mod(n, 2)==0, d1=d1+3
)
)
)
);
a=a+d1;
print1(a, ", ")
)
}
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CROSSREFS
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KEYWORD
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nonn,nice,easy
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AUTHOR
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STATUS
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approved
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