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A261953 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 "vertex to vertex" version; a(n) is the number of triangles added in the n-th generation. 8
1, 3, 9, 12, 18, 21, 27, 30, 36, 39, 45, 48, 54, 57, 63, 66, 72, 75, 81, 84, 90, 93, 99, 102, 108, 111, 117, 120, 126, 129, 135, 138, 144, 147, 153, 156, 162, 165, 171, 174, 180, 183, 189, 192, 198, 201, 207, 210, 216, 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             a(n)   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

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

Kival Ngaokrajang, Illustration of initial terms

FORMULA

a(0)=1, a(1)=3; for n >= 2, a(n)= a(n-1) + 6, if mod(n,2) = 0, otherwise a(n) = a(n-1) + 3.

Conjectures from Colin Barker, Sep 10 2015: (Start)

a(n) = (3*(-1+(-1)^n+6*n))/4.

a(n) = a(n-1)+a(n-2)-a(n-3) for n>3.

G.f.: (x^3+5*x^2+2*x+1) / ((x-1)^2*(x+1)).

(End)

a(n) = A032766(n)/3 for n>=1 (conjecture). - Michel Marcus, Sep 13 2015

PROG

(PARI) {a=3; print1("1, ", a, ", "); for(n=2, 100, if (Mod(n, 2)==0, a=a+6, a=a+3); print1(a, ", "))}

CROSSREFS

Cf. A032766, A008486, A248969, A249246.

Sequence in context: A274676 A310321 A310322 * A297001 A309394 A285564

Adjacent sequences:  A261950 A261951 A261952 * A261954 A261955 A261956

KEYWORD

nonn

AUTHOR

Kival Ngaokrajang, Sep 06 2015

STATUS

approved

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Last modified June 16 21:55 EDT 2021. Contains 345080 sequences. (Running on oeis4.)