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A261958
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Start with a single square for n=0; for the odd n-th generation add a square at each expandable vertex of the squares of the (n-1)-th generation (this is the "vertex to vertex" version); for the even n-th generation use the "side to vertex" version; a(n) is the number of squares added in the n-th generation.
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1
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1, 4, 12, 16, 24, 32, 28, 36, 32, 44, 44, 56, 56, 72, 60, 76, 64, 84, 76, 96, 88, 112, 92, 116, 96, 124, 108, 136, 120, 152, 124, 156, 128, 164, 140, 176, 152, 192, 156, 196, 160, 204, 172, 216, 184, 232, 188, 236, 192, 244, 204, 256, 216
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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-8)-a(n-10) for n>10.
G.f.: (x^10+4*x^9+3*x^8+4*x^7+4*x^6+16*x^5+12*x^4+12*x^3+11*x^2+4*x+1) / ((x-1)^2*(x+1)^2*(x^2+1)*(x^4+1)).
(End)
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PROG
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(PARI) {e=12; o=4; print1("1, ", o, ", ", e, ", "); for(n=3, 100, if (Mod(n, 2)==0, if (Mod(n, 8)==4, e=e+12); if (Mod(n, 8)==6, e=e+4); if (Mod(n, 8)==0, e=e+4); if (Mod(n, 8)==2, e=e+12); print1(e, ", "), if (Mod(n, 8)==3, o=o+12); if (Mod(n, 8)==5, o=o+16); if (Mod(n, 8)==7, o=o+4); if (Mod(n, 8)==1, o=o+8); 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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STATUS
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approved
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