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A122581 a(n) = a(n - 1) - 2*a(n - 2) + a(n - 3) - 4*a(n - 4) + 2*a(n - 5).

%I A122581 #21 Nov 28 2021 21:21:35
%S A122581 1,1,1,1,1,-2,-5,-2,4,13,19,-5,-50,-65,-20,118,283,187,-311,-914,
%T A122581 -1001,334,3040,4405,835,-8273,-17030,-11189,20068,60178,60427,-29165,
%U A122581 -192491,-274310,-39845,553798,1070812,635629,-1341437,-3836765,-3693914,2237287,12425356,16921054,1409755,-36343973
%N A122581 a(n) = a(n - 1) - 2*a(n - 2) + a(n - 3) - 4*a(n - 4) + 2*a(n - 5).
%C A122581 This recursion is inspired by Ulam's early experiments in derivative recursions.
%H A122581 G. C. Greubel, <a href="/A122581/b122581.txt">Table of n, a(n) for n = 1..1000</a>
%H A122581 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (1,-2,1,-4,2).
%F A122581 G.f.: x*(1+2*x^2+x^3+5*x^4)/(1-x+2*x^2-x^3+4*x^4-2*x^5). - _R. J. Mathar_, Nov 18 2007
%p A122581 A122581:= proc(n) option remember; if n <= 5 then 1; else A122581(n-1) -2*A122581(n-2)+A122581(n-3)+2*(-2*A122581(n-4)+A122581(n-5)); fi; end: seq(A122581(n),n=1..50) ; # _R. J. Mathar_, Sep 18 2007
%t A122581 a[n_]:= a[n]= If[n<6, 1, a[n-1] -2*a[n-2] +a[n-3] -2*(2*a[n-4] -a[n-5])];
%t A122581 Table[a[n], {n,50}]
%o A122581 (Sage)
%o A122581 @CachedFunction # a=A122581
%o A122581 def a(n): return 1 if (n<6) else a(n-1) -2*a(n-2) +a(n-3) -4*a(n-4) +2*a(n-5)
%o A122581 [a(n) for n in (1..50)] # _G. C. Greubel_, Nov 28 2021
%Y A122581 Cf. A122582, A122583, A122584.
%K A122581 sign
%O A122581 1,6
%A A122581 _Roger L. Bagula_, Sep 19 2006
%E A122581 Edited by _N. J. A. Sloane_, Oct 01 2006
%E A122581 More terms from _R. J. Mathar_, Sep 18 2007