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A261953
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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 side of the triangles of the (n-1)-th generation (this is the "side to side" 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, 18, 21, 27, 30, 36, 39, 45, 48, 54, 57, 63, 66, 72, 75, 81, 84, 90, 93, 99, 102, 108, 111, 117, 120, 126, 129, 135, 138, 144, 147, 153, 156, 162, 165, 171, 174, 180, 183, 189, 192, 198, 201, 207, 210, 216, 219
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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.
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 |
| V-V A008486 A248969 A261951 A261952 |
| S-V A261950 A008486 A008486 A261956 |
| V-S A249246 A008486 A008486 A261957 |
| S-S a(n) A261954 A261955 A008486 |
+-------------------------------------------------------+
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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Table of n, a(n) for n=0..49.
Kival Ngaokrajang, Illustration of initial terms
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FORMULA
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a(0)=1, a(1)=3; for n >= 2, a(n)= a(n-1) + 6, if mod(n,2) = 0, otherwise a(n) = a(n-1) + 3.
Conjectures from Colin Barker, Sep 10 2015: (Start)
a(n) = (3*(-1+(-1)^n+6*n))/4.
a(n) = a(n-1)+a(n-2)-a(n-3) for n>3.
G.f.: (x^3+5*x^2+2*x+1) / ((x-1)^2*(x+1)).
(End)
a(n) = A032766(n)/3 for n>=1 (conjecture). - Michel Marcus, Sep 13 2015
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PROG
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(PARI) {a=3; print1("1, ", a, ", "); for(n=2, 100, if (Mod(n, 2)==0, a=a+6, a=a+3); print1(a, ", "))}
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CROSSREFS
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Cf. A032766, A008486, A248969, A249246.
Sequence in context: A274676 A310321 A310322 * A297001 A309394 A285564
Adjacent sequences: A261950 A261951 A261952 * A261954 A261955 A261956
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KEYWORD
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nonn
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AUTHOR
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Kival Ngaokrajang, Sep 06 2015
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STATUS
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approved
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