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A299965
Number of triangles in a Star of David of size n.
2
0, 20, 118, 354, 788, 1480, 2490, 3878, 5704, 8028, 10910, 14410, 18588, 23504, 29218, 35790, 43280, 51748, 61254, 71858, 83620, 96600, 110858, 126454, 143448, 161900, 181870, 203418, 226604, 251488, 278130, 306590, 336928, 369204, 403478, 439810, 478260, 518888
OFFSET
0,2
COMMENTS
In a Star of David of size n, there are A135453(n) "size=1" triangles.
The number of matchstick units is A045946.
LINKS
Paolo Xausa, Table of n, a(n) for n = 0..10000 (corrected and extended original b-file from Colin Barker after data change).
FORMULA
a(n) = n*(10*n^2+9*n+1) = 2*A045950(n).
From Colin Barker, Apr 04 2019: (Start)
G.f.: 2*x*(10 + 19*x + x^2) / (1 - x)^4.
a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4) for n>3. (End)
E.g.f.: exp(x)*x*(20 + 39*x + 10*x^2). - Stefano Spezia, Sep 20 2024
EXAMPLE
For n=1, there are 12 (size=1) + 6 (size=4) + 2 (size=9) = 20 triangles.
MATHEMATICA
A299965[n_] := n*(n*(10*n + 9) + 1); Array[A299965, 50, 0] (* or *)
LinearRecurrence[{4, -6, 4, -1}, {0, 20, 118, 354}, 50] (* Paolo Xausa, Sep 18 2024 *)
PROG
(PARI) concat(0, Vec(2*x*(10 + 19*x + x^2) / (1 - x)^4 + O(x^40))) \\ Colin Barker, Apr 04 2019
CROSSREFS
For the total number of triangles in a different arrangement, see A002717 (for triangular matchstick), A045949 (for hexagonal matchstick).
Sequence in context: A377987 A258667 A357042 * A244289 A293880 A121040
KEYWORD
nonn,easy,less
AUTHOR
John King, Feb 22 2018
EXTENSIONS
Corrected by John King, Stefano Spezia, and Paolo Xausa, Sep 20 2024
STATUS
approved