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A261950
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Start with a single equilateral triangle for n=0; for the odd n-th generation add a triangle at each expandable vertex of the triangles of the (n-1)-th generation (this is the "side to vertex" version); for the even n-th generation use the "vertex to vertex" version; a(n) is the number of triangles added in the n-th generation.
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8
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1, 3, 9, 12, 30, 18, 45, 27, 66, 33, 81, 42, 102, 48, 117, 57, 138, 63, 153, 72, 174, 78, 189, 87, 210, 93, 225, 102, 246, 108, 261, 117, 282, 123, 297, 132, 318, 138, 333, 147, 354, 153, 369, 162, 390, 168, 405
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OFFSET
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0,2
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COMMENTS
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See a comment on V-V and V-S at A249246.
The overlap rules for the expansion are: (i) overlap within generation is allowed. (ii) overlap of different generations is prohibited.
There are a total of 16 combinations as shown in the table below:
+-------------------------------------------------------+
| Even n-th version V-V S-V V-S S-S |
+-------------------------------------------------------+
| Odd n-th version |
+-------------------------------------------------------+
Note: V-V = vertex to vertex, S-V = side to vertex,
V-S = vertex to side, S-S = side to side.
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LINKS
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FORMULA
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a(n) = a(n-2)+a(n-4)-a(n-6) for n>6.
G.f.: (7*x^6+3*x^5+20*x^4+9*x^3+8*x^2+3*x+1) / ((x-1)^2*(x+1)^2*(x^2+1)).
(End)
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PROG
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(PARI) {e=9; o=3; print1("1, ", o, ", ", e, ", "); for(n=3, 100, if (Mod(n, 2)==0, if (Mod(n, 4)==0, e=e+21); if (Mod(n, 4)==2, e=e+15); print1(e, ", "), if (Mod(n, 4)==3, o=o+9); if (Mod(n, 4)==1, o=o+6); print1(o, ", ")))}
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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