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A307253 Number of triangles larger than size=1 in a matchstick-made hexagon with side length n. 4
0, 0, 14, 62, 166, 346, 624, 1020, 1556, 2252, 3130, 4210, 5514, 7062, 8876, 10976, 13384, 16120, 19206, 22662, 26510, 30770, 35464, 40612, 46236, 52356, 58994, 66170, 73906, 82222, 91140, 100680, 110864, 121712, 133246, 145486, 158454, 172170, 186656, 201932 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

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

Index entries for linear recurrences with constant coefficients, signature (3,-2,-2,3,-1).

FORMULA

a(n) = floor(n*(14*n^2+9*n+2)/4)-6*n^2.

G.f.: 2*x^2*(4*x^2+10*x+7)/((x+1)*(x-1)^4).

a(n) = A045949(n) - A033581(n).

a(n) = 3*a(n-1) - 2*a(n-2) - 2*a(n-3) + 3*a(n-4) - a(n-5) for n>4. - Colin Barker, Apr 02 2019

MATHEMATICA

LinearRecurrence[{3, -2, -2, 3, -1}, {0, 0, 14, 62, 166}, 166] (* Metin Sariyar, Oct 27 2019 *)

PROG

(PARI) concat([0, 0], Vec(2*x^2*(7 + 10*x + 4*x^2) / ((1 - x)^4*(1 + x)) + O(x^40))) \\ Colin Barker, Apr 02 2019

CROSSREFS

Cf. A033581 (number of size=1 triangles), A045949 (total number of triangles).

The hexagon matchstick sequences are as follows: number of matchsticks: A045945; for T1 triangles: A033581; for larger triangles: this sequence and for total triangles: A045949. There are analogs for triangles (see A045943) and stars (see A045946).

Sequence in context: A189948 A252255 A025415 * A125849 A003695 A022674

Adjacent sequences:  A307250 A307251 A307252 * A307254 A307255 A307256

KEYWORD

nonn

AUTHOR

John King, Mar 31 2019

STATUS

approved

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Last modified May 28 13:20 EDT 2020. Contains 334683 sequences. (Running on oeis4.)