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A135687 a(n) = a(n-1) - A004001(n)*a(n-2), a(1) = 1, a(2) = 1.

%I A135687 #17 May 31 2022 16:28:24
%S A135687 1,1,-1,-3,0,12,12,-36,-96,120,792,-48,-6384,-6000,45072,93072,
%T A135687 -312576,-1243296,2195040,17114592,-9225888,-231715584,-102553152,
%U A135687 3141465024,4679762304,-42442213056,-112638647616,566436761280,2368655123136,-6694333057344,-44592815027520
%N A135687 a(n) = a(n-1) - A004001(n)*a(n-2), a(1) = 1, a(2) = 1.
%H A135687 G. C. Greubel, <a href="/A135687/b135687.txt">Table of n, a(n) for n = 1..500</a>
%F A135687 a(n) = a(n-1) - A004001(n)*a(n-2), with a(1) = a(2) = 1.
%t A135687 HC[n_]:= HC[n]= If[n<3, Fibonacci[n], HC[HC[n-1]] +HC[n -HC[n-1]]]; (*A004001*)
%t A135687 a[n_]:= a[n]= If[n<3, 1, a[n-1] - HC[n]*a[n-2]];
%t A135687 Table[a[n], {n, 40}]
%o A135687 (Sage)
%o A135687 @cached_function
%o A135687 def HC(n): # HC = A004001
%o A135687     if (n<3): return fibonacci(n)
%o A135687     else: return HC(HC(n-1)) +HC(n -HC(n-1))
%o A135687 @CachedFunction
%o A135687 def a(n): # A135688
%o A135687     if (n<3): return 1
%o A135687     else: return a(n-1) - HC(n)*a(n-2)
%o A135687 [a(n) for n in (1..40)] # _G. C. Greubel_, Nov 25 2021
%Y A135687 Cf. A004001, A135688.
%K A135687 sign,less
%O A135687 1,4
%A A135687 _Roger L. Bagula_, Feb 19 2008