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.

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

Offset: 0

Author

Kival Ngaokrajang, Sep 06 2015

Keywords

• nonn

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

Crossrefs

Cf. A008486, A248969, A249246, A245094.

Programs

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, ", "))}

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)