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!)
 A261954 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 "side to vertex" version; a(n) is the number of triangles added in the n-th generation. 8
 1, 3, 3, 6, 12, 15, 21, 18, 30, 27, 39, 30, 48, 39, 57, 42, 66, 51, 75, 54, 84, 63, 93, 66, 102, 75, 111, 78, 120, 87, 129, 90, 138, 99, 147, 102, 156, 111, 165, 114, 174, 123, 183, 126, 192, 135, 201, 138, 210, 147, 219 (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  A261952 | |      S-V           A261950  A008486  A008486  A261956 | |      V-S           A249246  A008486  A008486  A261957 | |      S-S           A261953    a(n)   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 Index entries for linear recurrences with constant coefficients, signature (0,1,0,1,0,-1). FORMULA a(0) = 1, a(1) = 3; for even n >= 2, a(n) = 9*(n/2-1) + 3 or a(n) = A017197(n/2-1); for odd n >= 3, a(n) = a(n-2) + 9, if mod(n,4) = 1 otherwise a(n) = a(n-2) + 3. Conjectures from Colin Barker, Sep 10 2015: (Start) a(n) = a(n-2)+a(n-4)-a(n-6) for n>6. G.f.: (7*x^6+6*x^5+8*x^4+3*x^3+2*x^2+3*x+1) / ((x-1)^2*(x+1)^2*(x^2+1)). (End) PROG (PARI) a=3; print1("1, ", a, ", "); for (n=2, 100, if (Mod(n, 4)==0||Mod(n, 4)==2, print1(9*(n/2-1)+3, ", "), if (Mod(n, 4)==1, a=a+9, a=a+3); print1(a, ", "))) CROSSREFS Cf. A008486, A017197, A248969, A249246. Sequence in context: A094305 A057963 A250301 * A112434 A050067 A309399 Adjacent sequences:  A261951 A261952 A261953 * A261955 A261956 A261957 KEYWORD nonn,easy 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 13 20:25 EDT 2021. Contains 345009 sequences. (Running on oeis4.)