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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

Table of n, a(n) for n=0..50.

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

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Last modified June 13 20:25 EDT 2021. Contains 345009 sequences. (Running on oeis4.)