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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

Table of n, a(n) for n=0..49.

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

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