A154407 a(n) = 5*2^(n-1) + 3*6^n/2.
4, 14, 64, 344, 1984, 11744, 70144, 420224, 2520064, 15117824, 90701824, 544200704, 3265183744, 19591061504, 117546287104, 705277558784, 4231665025024, 25389989494784, 152339935657984, 914039611326464, 5484237662715904
Offset: 0
Examples
Sequence A154383 and its k-th iterated difference in the k-th row are ...1.....0.....4.....2.....16......8.....64.....32....256....128...1024. ..-1.....4....-2....14.....-8.....56....-32....224...-128....896...-512. ...5....-6....16...-22.....64....-88....256...-352...1024..-1408...4096. .-11....22...-38....86...-152....344...-608...1376..-2432...5504..-9728. ..33...-60...124..-238....496...-952...1984..-3808...7936.-15232..31744. .-93...184..-362...734..-1448...2936..-5792..11744.-23168..46976.-92672. .277..-546..1096.-2182...4384..-8728..17536.-34912..70144.-139648.280576. The sequence is the diagonal T(k,k+2) in this array.
Links
- Vincenzo Librandi, Table of n, a(n) for n = 0..150
- Index entries for linear recurrences with constant coefficients, signature (8, -12).
Programs
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Magma
[5*2^(n-1)+3*6^n/2: n in [0..40]]; // Vincenzo Librandi, Apr 28 2011
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Maple
A154407:=n->5*2^(n-1)+3*6^n/2; seq(A154407(n), n=0..50); # Wesley Ivan Hurt, Nov 13 2013
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Mathematica
Table[5*2^(n-1)+3*6^n/2, {n,0,50}] (* Wesley Ivan Hurt, Nov 13 2013 *)
Formula
a(n+1) = 6*a(n) - 10*2^n.
a(n) = 6*a(n) - 5*A020714(n+1).
G.f.: 2*(2 - 9*x)/((6*x-1)*(2*x-1)). - R. J. Mathar, May 21 2009
E.g.f.: (1/2)*( 5*exp(2*x) + 3*exp(6*x) ). - G. C. Greubel, Sep 16 2016
Extensions
Edited by R. J. Mathar, May 21 2009
Comments