cp's OEIS Frontend

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

%I A281698 #32 Dec 09 2017 03:19:41
%S A281698 5,14,55,269,1465,8369,48865,288449,1713025,10210049,60993025,
%T A281698 364899329,2185181185,13094268929,78498422785,470721937409,
%U A281698 2823257554945,16935249707009,101594317062145,609497180274689,3656708198498305,21939149668876289,131630499945775105
%N A281698 a(n) = 5*2^(n-1) + 2^(2*n-1) + 6^n + 1.
%C A281698 Similar to A279511 Sierpinski square-based pyramid but with tetrahedral openings as found in the structure of the Sierpinski octahedron A279512.
%H A281698 Colin Barker, <a href="/A281698/b281698.txt">Table of n, a(n) for n = 0..1000</a>
%H A281698 Wikipedia, <a href="https://en.wikipedia.org/wiki/Sierpinski_triangle">Sierpinski triangle</a>, see section on higher dimensional analogs.
%H A281698 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (13,-56,92,-48).
%F A281698 From _Colin Barker_, Jan 28 2017: (Start)
%F A281698 a(n) = 13*a(n-1) - 56*a(n-2) + 92*a(n-3) - 48*a(n-4) for n>3.
%F A281698 G.f.: (5 - 51*x + 153*x^2 - 122*x^3) / ((1 - x)*(1 - 2*x)*(1 - 4*x)*(1 - 6*x)).
%F A281698 (End)
%p A281698 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 A281698 Table[5*2^(n - 1) + 2^(2 n - 1) + 6^n + 1, {n, 0, 22}] (* or *)
%t A281698 LinearRecurrence[{13, -56, 92, -48}, {5, 14, 55, 269}, 23] (* or *)
%t A281698 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 A281698 (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 A281698 (PARI) a(n) = 5*2^(n-1) + 2^(2*n-1) + 6^n + 1 \\ _Charles R Greathouse IV_, Jan 29 2017
%Y A281698 Cf. A000330, A047999, A279511, A279512.
%K A281698 nonn,easy
%O A281698 0,1
%A A281698 _Steven Beard_, Jan 27 2017