cp's OEIS Frontend

A249169 Fibonacci 16-step numbers, a(n) = a(n-1) + a(n-2) + ... + a(n-16).

%I A249169 #29 Apr 05 2018 23:17:12
%S A249169 1,1,2,4,8,16,32,64,128,256,512,1024,2048,4096,8192,16384,32768,65535,
%T A249169 131069,262136,524268,1048528,2097040,4194048,8388032,16775936,
%U A249169 33551616,67102720,134204416,268406784,536809472,1073610752,2147205120,4294377472,8588689409
%N A249169 Fibonacci 16-step numbers, a(n) = a(n-1) + a(n-2) + ... + a(n-16).
%H A249169 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 A249169 <a href="/index/Rec#order_16">Index entries for linear recurrences with constant coefficients</a>, signature (1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1).
%F A249169 a(n) = a(n-1) + a(n-2) + ... + a(n-16).
%F A249169 G.f.: -x^15 / (x^16+x^15+x^14+x^13+x^12+x^11+x^10+x^9+x^8+x^7+x^6+x^5 +x^4+x^3+x^2+x-1). - _Alois P. Heinz_, Oct 23 2014
%p A249169 a:= proc(n) option remember; `if`(n<15, 0,
%p A249169       `if`(n=15, 1, add(a(n-j), j=1..16)))
%p A249169     end:
%p A249169 seq(a(n), n=15..50);  # _Alois P. Heinz_, Oct 23 2014
%t A249169 CoefficientList[Series[-1 /(x^16 + x^15 + x^14 + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x - 1), {x, 0, 50}], x] (* _Vincenzo Librandi_, Nov 21 2014 *)
%Y A249169 Other k-step Fibonacci sequences: Cf. A000045, A000213, A000288, A000322, A000383, A060455, A123526, A127193, A127194, A168083, A207539, A168084, A220469, A220493.
%K A249169 nonn,easy
%O A249169 15,3
%A A249169 _Alan N. Inglis_, Oct 22 2014