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A220493 Fibonacci 15-step numbers, a(n) = a(n-1) + a(n-2) + ... + a(n-15).

%I A220493 #39 Feb 11 2020 10:07:45
%S A220493 1,1,2,4,8,16,32,64,128,256,512,1024,2048,4096,8192,16384,32767,65533,
%T A220493 131064,262124,524240,1048464,2096896,4193728,8387328,16774400,
%U A220493 33548288,67095552,134189056,268374016,536739840,1073463296,2146893825,4293722117,8587313170
%N A220493 Fibonacci 15-step numbers, a(n) = a(n-1) + a(n-2) + ... + a(n-15).
%C A220493 Also called Pentadecanacci 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 A220493 Robert Israel, <a href="/A220493/b220493.txt">Table of n, a(n) for n = 1..3320</a>
%H A220493 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 A220493 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 A220493 <a href="/index/Rec#order_15">Index entries for linear recurrences with constant coefficients</a>, signature (1,1,1,1,1,1,1,1,1,1,1,1,1,1,1).
%F A220493 G.f.: x/(1-Sum_{k=1..15} x^k). - _Robert Israel_, Feb 19 2019
%p A220493 f:= gfun:-rectoproc({a(n) = add(a(n-i),i=1..15), seq(a(n)=0,n=-14..0),a(1)=1},a(n),remember):
%p A220493 map(f, [$1..100]); # _Robert Israel_, Feb 19 2019
%t A220493 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[15, 50] (* _T. D. Noe_, Feb 20 2013 *)
%Y A220493 Cf. A000045 (Fibonacci), A000073 (tribonacci), A000078 (tetranacci), A001591 (pentanacci).
%K A220493 nonn,easy
%O A220493 1,3
%A A220493 _Ruskin Harding_, Feb 20 2013