A261955 - OEIS

A261955

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 side" version; a(n) is the number of triangles added in the n-th generation.

1, 3, 6, 15, 12, 24, 15, 33, 21, 45, 39, 72, 36, 78, 39, 87, 45, 99, 63, 126, 60, 132, 63, 141, 69, 153, 87, 180, 84, 186, 87, 195, 93, 207, 111, 234, 108, 240, 111, 249, 117, 261, 135, 288, 132, 294, 135, 303, 141, 315, 159

(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 A261954 a(n) 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..50.

Kival Ngaokrajang, Illustration of initial terms

FORMULA

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

a(n) = a(n-2)+a(n-8)-a(n-10) for n>13.

G.f.: -(3*x^13+9*x^12-15*x^11-13*x^10-9*x^9-5*x^8-9*x^7-3*x^6-9*x^5-6*x^4-12*x^3-5*x^2-3*x-1) / ((x-1)^2*(x+1)^2*(x^2+1)*(x^4+1)).

(End)

PROG

(PARI) {e=12; o=24; print1("1, 3, 6, 15, ", e, ", ", o, ", "); for(n=6, 100, if (Mod(n, 2)==0, if (Mod(n, 8)==6, e=e+3); if (Mod(n, 8)==0, e=e+6); if (Mod(n, 8)==2, e=e+18); if (Mod(n, 8)==4, e=e-3); Print1(e, ", "), if (Mod(n, 8)==7, o=o+9); if (Mod(n, 8)==1, o=o+12); if (Mod(n, 8)==3, o=o+27); if (Mod(n, 8)==5, o=o+6); print1(o, ", ")))}

CROSSREFS

Cf. A008486, A248969, A249246.

Sequence in context: A334042 A066107 A162276 * A144615 A088698 A105802

Adjacent sequences: A261952 A261953 A261954 * A261956 A261957 A261958

KEYWORD

nonn

AUTHOR

Kival Ngaokrajang, Sep 06 2015

STATUS

approved