A281699 Sierpinski stellated octahedron numbers: a(n) = 2*(-3*2^(n+1) + 2^(2n+3) + 5).

14, 50, 218, 938, 3914, 16010, 64778, 260618, 1045514, 4188170, 16764938, 67084298, 268386314, 1073643530, 4294770698, 17179475978, 68718690314, 274876334090, 1099508482058, 4398040219658, 17592173461514, 70368719011850, 281474926379018, 1125899806179338, 4503599426043914, 18014398106828810

Offset: 0

Author

Steven Beard, Jan 27 2017

Keywords

• nonn
• easy

Comments

Stella octangula with Sierpinski recursion.

Links

• Colin Barker, Table of n, a(n) for n = 0..1000
• Wikipedia, Sierpinski triangle, see section on higher dimensional analogs.
• Index entries for linear recurrences with constant coefficients, signature (7,-14,8).

Crossrefs

Cf. A007588, A027693, A052539, A052548, A067771, A178789, A233774, A279511.

Programs

Mathematica

Table[8 (2^(2 n + 1) + 2) - 6 (2^(n + 1) + 1), {n, 0, 25}] (* or *)
LinearRecurrence[{7, -14, 8}, {14, 50, 218}, 26] (* or *)
CoefficientList[Series[2 (7 - 24 x + 32 x^2)/((1 - x) (1 - 2 x) (1 - 4 x)), {x, 0, 25}], x] (* Michael De Vlieger, Jan 28 2017 *)

PARI

Vec(2*(7 - 24*x + 32*x^2) / ((1 - x)*(1 - 2*x)*(1 - 4*x)) + O(x^30)) \\ Colin Barker, Jan 28 2017

PARI

a(n) = 16*4^n - 12*2^n + 10 \\ Charles R Greathouse IV, Jan 29 2017

Formula

a(n) = 8*(2^(2*n+1)+2) - 6*(2^(n+1)+1).

From Colin Barker, Jan 28 2017: (Start)

a(n) = 7*a(n-1) - 14*a(n-2) + 8*a(n-3) for n>2.

G.f.: 2*(7 - 24*x + 32*x^2) / ((1 - x)*(1 - 2*x)*(1 - 4*x)).

(End)