A281698 a(n) = 5*2^(n-1) + 2^(2*n-1) + 6^n + 1.

5, 14, 55, 269, 1465, 8369, 48865, 288449, 1713025, 10210049, 60993025, 364899329, 2185181185, 13094268929, 78498422785, 470721937409, 2823257554945, 16935249707009, 101594317062145, 609497180274689, 3656708198498305, 21939149668876289, 131630499945775105

Offset: 0

Author

Steven Beard, Jan 27 2017

Keywords

• nonn
• easy

Comments

Similar to A279511 Sierpinski square-based pyramid but with tetrahedral openings as found in the structure of the Sierpinski octahedron A279512.

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 (13,-56,92,-48).

Crossrefs

Cf. A000330, A047999, A279511, A279512.

Programs

Maple

A281698:=n->5*2^(n-1) + 2^(2*n-1) + 6^n + 1: seq(A281698(n), n=0..30); # Wesley Ivan Hurt, Apr 09 2017

Mathematica

Table[5*2^(n - 1) + 2^(2 n - 1) + 6^n + 1, {n, 0, 22}] (* or *)
LinearRecurrence[{13, -56, 92, -48}, {5, 14, 55, 269}, 23] (* or *)
CoefficientList[Series[(5 - 51 x + 153 x^2 - 122 x^3)/((1 - x) (1 - 2 x) (1 - 4 x) (1 - 6 x)), {x, 0, 22}], x] (* Michael De Vlieger, Jan 28 2017 *)

PARI

Vec((5 - 51*x + 153*x^2 - 122*x^3) / ((1 - x)*(1 - 2*x)*(1 - 4*x)*(1 - 6*x)) + O(x^30)) \\ Colin Barker, Jan 28 2017

PARI

a(n) = 5*2^(n-1) + 2^(2*n-1) + 6^n + 1 \\ Charles R Greathouse IV, Jan 29 2017

Formula

From Colin Barker, Jan 28 2017: (Start)

a(n) = 13*a(n-1) - 56*a(n-2) + 92*a(n-3) - 48*a(n-4) for n>3.

G.f.: (5 - 51*x + 153*x^2 - 122*x^3) / ((1 - x)*(1 - 2*x)*(1 - 4*x)*(1 - 6*x)).

(End)