The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation. Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A261952 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 "side to side" version; a(n) is the number of triangles added in the n-th generation. 8
 1, 3, 9, 18, 18, 24, 27, 33, 36, 42, 45, 51, 54, 60, 63, 69, 72, 78, 81, 87, 90, 96, 99, 105, 108, 114, 117, 123, 126, 132, 135, 141, 144, 150, 153, 159, 162, 168, 171, 177, 180, 186, 189, 195, 198, 204, 207, 213, 216, 222 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS 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    a(n)  | |      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. For n > 4, a(n) = A245094(n+1). LINKS Kival Ngaokrajang, Illustration of initial terms FORMULA Conjectures from Colin Barker, Sep 10 2015: (Start) a(n) = 3*(1-(-1)^n+6*n)/4 for n>3. a(n) = a(n-1)+a(n-2)-a(n-3) for n>6. G.f.: (3*x^6-3*x^5-6*x^4+7*x^3+5*x^2+2*x+1) / ((x-1)^2*(x+1)). (End) PROG (PARI) {a=18; print1("1, 3, 9, 18, ", a, ", "); for(n=5, 100, if (Mod(n, 2)==0, a=a+3, a=a+6); print1(a, ", "))} CROSSREFS Cf. A008486, A248969, A249246, A245094. Sequence in context: A109228 A103162 A310331 * A066006 A323199 A310332 Adjacent sequences:  A261949 A261950 A261951 * A261953 A261954 A261955 KEYWORD nonn AUTHOR Kival Ngaokrajang, Sep 06 2015 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified June 22 04:06 EDT 2021. Contains 345367 sequences. (Running on oeis4.)