The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

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