A154407 - OEIS

%I #16 Jun 30 2023 00:08:45

%S 4,14,64,344,1984,11744,70144,420224,2520064,15117824,90701824,

%T 544200704,3265183744,19591061504,117546287104,705277558784,

%U 4231665025024,25389989494784,152339935657984,914039611326464,5484237662715904

%N a(n) = 5*2^(n-1) + 3*6^n/2.

%C One of the diagonals of the n-th differences of A154383.

%H Vincenzo Librandi, <a href="/A154407/b154407.txt">Table of n, a(n) for n = 0..150</a>

%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (8, -12).

%F a(n+1) = 6*a(n) - 10*2^n.

%F a(n) = 6*a(n) - 5*A020714(n+1).

%F G.f.: 2*(2 - 9*x)/((6*x-1)*(2*x-1)). - _R. J. Mathar_, May 21 2009

%F E.g.f.: (1/2)*( 5*exp(2*x) + 3*exp(6*x) ). - _G. C. Greubel_, Sep 16 2016

%e Sequence A154383 and its k-th iterated difference in the k-th row are

%e ...1.....0.....4.....2.....16......8.....64.....32....256....128...1024.

%e ..-1.....4....-2....14.....-8.....56....-32....224...-128....896...-512.

%e ...5....-6....16...-22.....64....-88....256...-352...1024..-1408...4096.

%e .-11....22...-38....86...-152....344...-608...1376..-2432...5504..-9728.

%e ..33...-60...124..-238....496...-952...1984..-3808...7936.-15232..31744.

%e .-93...184..-362...734..-1448...2936..-5792..11744.-23168..46976.-92672.

%e .277..-546..1096.-2182...4384..-8728..17536.-34912..70144.-139648.280576.

%e The sequence is the diagonal T(k,k+2) in this array.

%p A154407:=n->5*2^(n-1)+3*6^n/2; seq(A154407(n), n=0..50); # _Wesley Ivan Hurt_, Nov 13 2013

%t Table[5*2^(n-1)+3*6^n/2, {n,0,50}] (* _Wesley Ivan Hurt_, Nov 13 2013 *)

%o (Magma) [5*2^(n-1)+3*6^n/2: n in [0..40]]; // _Vincenzo Librandi_, Apr 28 2011

%K nonn,easy

%O 0,1

%A _Paul Curtz_, Jan 09 2009

%E Edited by _R. J. Mathar_, May 21 2009