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A254835
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Total number of nonagons in a variant of a nonagon expansion ("side-to-side", two consecutive sides) after n iterations.
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1
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2, 4, 7, 11, 16, 22, 29, 37, 46, 56, 67, 79, 92, 106, 121, 133, 136, 144, 153, 161, 170, 180, 187, 197, 206, 216, 225, 233, 242, 248, 259, 269, 278, 286, 295, 305, 314, 322, 331, 341, 350, 358, 367, 377, 386, 394, 403, 413, 422, 430, 439, 449, 458, 466, 475, 485, 494, 502
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OFFSET
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1,1
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COMMENTS
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Two irregular star-shaped 18-gons appear for n = 17.
There are also rare types of polygons appearing for n >= 16. See illustrations.
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LINKS
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Table of n, a(n) for n=1..58.
Kival Ngaokrajang, Illustration of initial terms, Rare type polygons
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FORMULA
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Conjectures from Colin Barker, Feb 08 2015: (Start)
a(n) = 2*a(n-1)-2*a(n-2)+2*a(n-3)-a(n-4) for n>21.
G.f.: -x*(2*x^33 -4*x^32 +4*x^31 -6*x^30 +4*x^29 +2*x^26 -4*x^25 +4*x^24 -4*x^23 +2*x^22 -2*x^20 -4*x^19 +8*x^18 -2*x^17 +8*x^16 +2*x^15 -2*x^14 -2*x^13 -2*x^12 -2*x^11 -2*x^10 -2*x^9 -2*x^8 -2*x^7 -2*x^6 -2*x^5 -2*x^4 -x^3 -3*x^2 -2) / ((x -1)^2*(x^2 +1)).
(End)
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PROG
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(PARI){a=259; print1("2, 4, 7, 11, 16, 22, 29, 37, 46, 56, 67, 79, 92, 106, 121, 133, 136, 144, 153, 161, 170, 180, 187, 197, 206, 216, 225, 233, 242, 248, ", a, ", "); for(n=32, 100, if(Mod(n, 4)==0, d=10, if(Mod(n, 4)==1, d=9, if(Mod(n, 4)==2, d=8, d=9))); a=a+d; print1(a, ", "))}
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CROSSREFS
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Cf. A061777 (Triangle expansion, vertex-to-vertex, 3 vertices), A179178 (Triangle expansion, side-to-side, 2 sides), A253687 (Pentagon expansion, side-to-side, 2 consecutive sides and 1 isolated side), A253688 (Pentagon expansion, vertex-to-vertex, 2 consecutive vertices and 1 isolated vertex), A253547 (Hexagon expansion, vertex-to-vertex, 2 vertices separated by 1 vertex), A253895 and A253896 (Octagon expansion).
Sequence in context: A337919 A025733 A025716 * A025725 A025732 A025739
Adjacent sequences: A254832 A254833 A254834 * A254836 A254837 A254838
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KEYWORD
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nonn
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AUTHOR
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Kival Ngaokrajang, Feb 08 2015
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STATUS
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approved
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