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 A261951 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 "vertex to vertex" version); for the even n-th generation use the "vertex to side" version; a(n) is the number of triangles added in the n-th generation. 8
 1, 3, 9, 12, 24, 24, 39, 27, 54, 33, 69, 42, 84, 54, 99, 57, 114, 63, 129, 72, 144, 84, 159, 87, 174, 93, 189, 102, 204, 114, 219, 117, 234, 123, 249, 132, 264, 144, 279, 147, 294, 153, 309, 162, 324, 174, 339, 177, 354 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS 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                                     | |      V-V           A008486  A248969    a(n)   A261952 | |      S-V           A261950  A008486  A008486  A261956 | |      V-S           A249246  A008486  A008486  A261957 | |      S-S           A261953  A261954  A261955  A008486 | +-------------------------------------------------------+ Note: V-V = vertex to vertex, S-V = side to vertex,       V-S = vertex to side,   S-S = side to side. LINKS Kival Ngaokrajang, Illustration of initial terms FORMULA Conjectures from Colin Barker, Sep 10 2015: (Start) a(n) = a(n-2)+a(n-8)-a(n-10) for n>10. G.f.: (7*x^10+3*x^9+14*x^8+3*x^7+15*x^6+12*x^5+15*x^4+9*x^3+8*x^2+3*x+1) / ((x-1)^2*(x+1)^2*(x^2+1)*(x^4+1)). (End) PROG (PARI) {e=9; o=3; print1("1, ", o, ", ", e, ", "); for(n=3, 100, if (Mod(n, 2)==0, e=e+15; print1(e, ", "), if (Mod(n, 8)==3, o=o+9); if (Mod(n, 8)==5, o=o+12); if (Mod(n, 8)==7, o=o+3); if (Mod(n, 8)==1, o=o+6); print1(o, ", ")))} CROSSREFS Cf. A008486, A248969, A249246. Sequence in context: A022379 A303192 A261957 * A308422 A081601 A244018 Adjacent sequences:  A261948 A261949 A261950 * A261952 A261953 A261954 KEYWORD nonn AUTHOR Kival Ngaokrajang, Sep 06 2015 STATUS approved

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Last modified May 15 10:54 EDT 2021. Contains 343909 sequences. (Running on oeis4.)