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

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A281698 a(n) = 5*2^(n-1) + 2^(2*n-1) + 6^n + 1. 2

%I

%S 5,14,55,269,1465,8369,48865,288449,1713025,10210049,60993025,

%T 364899329,2185181185,13094268929,78498422785,470721937409,

%U 2823257554945,16935249707009,101594317062145,609497180274689,3656708198498305,21939149668876289,131630499945775105

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

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

%H Colin Barker, <a href="/A281698/b281698.txt">Table of n, a(n) for n = 0..1000</a>

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Sierpinski_triangle">Sierpinski triangle</a>, see section on higher dimensional analogs.

%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (13,-56,92,-48).

%F From _Colin Barker_, Jan 28 2017: (Start)

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

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

%F (End)

%p 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

%t Table[5*2^(n - 1) + 2^(2 n - 1) + 6^n + 1, {n, 0, 22}] (* or *)

%t LinearRecurrence[{13, -56, 92, -48}, {5, 14, 55, 269}, 23] (* or *)

%t 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 *)

%o (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

%o (PARI) a(n) = 5*2^(n-1) + 2^(2*n-1) + 6^n + 1 \\ _Charles R Greathouse IV_, Jan 29 2017

%Y Cf. A000330, A047999, A279511, A279512.

%K nonn,easy

%O 0,1

%A _Steven Beard_, Jan 27 2017

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.

License Agreements, Terms of Use, Privacy Policy. .

Last modified July 8 19:20 EDT 2020. Contains 335524 sequences. (Running on oeis4.)