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A299965 Number of triangles in a Star of David of size n. 3
0, 20, 118, 348, 764, 1420, 2370, 3668, 5368, 7524, 10190, 13420, 17268, 21788, 27034, 33060, 39920, 47668, 56358, 66044, 76780, 88620, 101618, 115828, 131304, 148100, 166270, 185868, 206948, 229564, 253770, 279620, 307168, 336468, 367574, 400540, 435420, 472268 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

In a Star of David of size n, there are A135453(n) "size=1" triangles and 2*A228887(n) "size>1" triangles. See formula.

The number of matchstick units is A045946.

LINKS

Colin Barker, Table of n, a(n) for n = 0..1000

John King, Star a=6, 84 matches, 118 triangles

Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).

FORMULA

a(n) = 9*n^3 + 12*n^2 - n.

a(n) = A135453(n) + 2 * A228887(n).

From Colin Barker, Apr 04 2019: (Start)

G.f.: 2*x*(10 - x)*(1 + 2*x) / (1 - x)^4.

a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4) for n>3.

(End)

EXAMPLE

For n=1, there are 12 (size=1) + 6 (size=4) + 2 (size=9) = 20 triangles.

PROG

(PARI) concat(0, Vec(2*x*(10 - x)*(1 + 2*x) / (1 - x)^4 + O(x^40))) \\ Colin Barker, Apr 04 2019

CROSSREFS

Cf. A045946, A135453, A228887.

For the total number of triangles in a different arrangement, see A002717 (for triangular matchstick), A045949 (for hexagonal matchstick).

Sequence in context: A220928 A206368 A258667 * A244289 A293880 A121040

Adjacent sequences:  A299962 A299963 A299964 * A299966 A299967 A299968

KEYWORD

nonn,easy

AUTHOR

John King, Feb 22 2018

STATUS

approved

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Last modified January 24 13:24 EST 2020. Contains 331193 sequences. (Running on oeis4.)