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A122583 a(n) = a(n - 1) - 2*a(n - 2) + a(n - 3) - 6*a(n - 4) + 3*a(n - 5).

%I A122583 #22 Jun 09 2025 14:50:46
%S A122583 1,1,1,1,1,-3,-7,-3,5,25,45,-3,-107,-191,-175,253,1045,1189,-171,
%T A122583 -3547,-7527,-4603,11497,33945,40869,-10487,-141071,-248407,-120131,
%U A122583 421141,1227961,1332777,-726439,-5051271,-8369959,-3306635,16738977,43110597,41391949,-33360335,-183387403,-283721435
%N A122583 a(n) = a(n - 1) - 2*a(n - 2) + a(n - 3) - 6*a(n - 4) + 3*a(n - 5).
%C A122583 This recursion is inspired by Ulam's early experiments in derivative recursions.
%H A122583 G. C. Greubel, <a href="/A122583/b122583.txt">Table of n, a(n) for n = 1..1000</a>
%H A122583 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (1,-2,1,-6,3).
%F A122583 G.f.: x*(1 +2*x^2 +x^3 +7*x^4)/(1 -x +2*x^2 -x^3 +6*x^4 -3*x^5). - Maksym Voznyy (voznyy(AT)mail.ru), Aug 11 2009
%p A122583 A122583:= proc(n) option remember; if n <= 5 then 1; else A122583(n-1) -2*A122583(n-2)+A122583(n-3)+3*(-2*A122583(n-4)+A122583(n-5)); fi; end: seq(A122583(n), n=1..50) ; # _R. J. Mathar_, Sep 18 2007
%t A122583 a[n_]:= a[n]= If[n<6, 1, a[n-1] -2*a[n-2] +a[n-3] -6*a[n-4] +3*a[n-5]];
%t A122583 Table[a[n], {n, 50}]
%t A122583 LinearRecurrence[{1,-2,1,-6,3},{1,1,1,1,1},50] (* _Harvey P. Dale_, Jun 09 2025 *)
%o A122583 (Magma) [n le 5 select 1 else Self(n-1) -2*Self(n-2) +Self(n-3) -6*Self(n-4) +3*Self(n-5): n in [1..50]]; // _G. C. Greubel_, Nov 28 2021
%o A122583 (Sage)
%o A122583 @CachedFunction # a=A122583
%o A122583 def a(n): return 1 if (n<6) else a(n-1) -2*a(n-2) +a(n-3) -6*a(n-4) +3*a(n-5)
%o A122583 [a(n) for n in (1..50)] # _G. C. Greubel_, Nov 28 2021
%Y A122583 Cf. A122581, A122582, A122584.
%K A122583 sign
%O A122583 1,6
%A A122583 _Roger L. Bagula_, Sep 19 2006
%E A122583 Edited by _N. J. A. Sloane_, Oct 01 2006
%E A122583 More terms from _R. J. Mathar_, Sep 18 2007