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A220469 Fibonacci 14-step numbers, a(n) = a(n-1) + a(n-2) + ... + a(n-14).

%I A220469 #65 Apr 05 2018 23:19:11
%S A220469 1,1,2,4,8,16,32,64,128,256,512,1024,2048,4096,8192,16383,32765,65528,
%T A220469 131052,262096,524176,1048320,2096576,4193024,8385792,16771072,
%U A220469 33541120,67080192,134156288,268304384,536592385,1073152005,2146238482,4292345912,8584429728
%N A220469 Fibonacci 14-step numbers, a(n) = a(n-1) + a(n-2) + ... + a(n-14).
%C A220469 Also called tetradecanacci numbers. In previous similar sequences, a(1),...,a(n-1) have been set equal to zero and a(n)=1. For example, A168084 (Fibonacci 13-step numbers) has 12 0's as the first 12 terms and a(13)=1.
%H A220469 M. Janjic, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL18/Janjic/janjic63.html">On Linear Recurrence Equations Arising from Compositions of Positive Integers</a>, J. Int. Seq. 18 (2015) # 15.4.7
%H A220469 Tony D. Noe and Jonathan Vos Post, <a href="http://www.cs.uwaterloo.ca/journals/JIS/VOL8/Noe/noe5.html">Primes in Fibonacci n-step and Lucas n-step Sequences,</a> J. of Integer Sequences, Vol. 8 (2005), Article 05.4.4
%H A220469 <a href="/index/Rec#order_14">Index entries for linear recurrences with constant coefficients</a>, signature (1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1).
%t A220469 FibonacciSequence[n_, kMax_] := Module[{a, s}, a = Join[{1}, Table[0, {n - 1}]]; lst = {}; Table[s = Plus @@ a; a = RotateLeft[a]; a[[n]] = s, {k, 1, kMax}]]; FibonacciSequence[14, 50] (* _T. D. Noe_, Feb 20 2013 *)
%t A220469 Drop[LinearRecurrence[PadRight[{},14,1],Join[PadRight[{},13,0],{1}],50],13] (* _Harvey P. Dale_, Feb 25 2013 *)
%t A220469 LinearRecurrence[{1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1},{1, 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096},35] (* _Ray Chandler_, Aug 03 2015 *)
%Y A220469 Cf. A000045 (Fibonacci), A000073 (tribonacci), A000078 (tetranacci), A001591 (pentanacci).
%K A220469 nonn
%O A220469 1,3
%A A220469 _Ruskin Harding_, Feb 20 2013