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A135688 a(n) = A004001(n)*a(n-1) + a(n-2), for n > 2, with a(1) = a(2) = 1.

%I A135688 #16 May 16 2022 11:02:23
%S A135688 1,1,3,7,24,103,436,1847,9671,59873,428782,3061347,24919558,202417811,
%T A135688 1644262046,13356514179,121852889657,1231885410749,13672592407896,
%U A135688 165302994305501,1997308524073908,26130313807266305,367821701825802178
%N A135688 a(n) = A004001(n)*a(n-1) + a(n-2), for n > 2, with a(1) = a(2) = 1.
%H A135688 G. C. Greubel, <a href="/A135688/b135688.txt">Table of n, a(n) for n = 1..500</a>
%F A135688 a(n) = A004001(n)*a(n-1) + a(n-2), for n > 2, with a(1) = a(2) = 1.
%t A135688 HC[n_]:= HC[n]= If[n<3, Fibonacci[n], HC[HC[n-1]] +HC[n -HC[n-1]]]; (*A004001*)
%t A135688 a[n_] := a[n] = If[n<3, 1, HC[n]*a[n-1] + a[n-2]];
%t A135688 Table[a[n], {n, 40}]
%o A135688 (Sage)
%o A135688 @cached_function
%o A135688 def HC(n): # HC = A004001
%o A135688     if (n<3): return fibonacci(n)
%o A135688     else: return HC(HC(n-1)) +HC(n -HC(n-1))
%o A135688 @CachedFunction
%o A135688 def a(n): # A135688
%o A135688     if (n<3): return 1
%o A135688     else: return HC(n)*a(n-1) + a(n-2)
%o A135688 [a(n) for n in (1..40)] # _G. C. Greubel_, Nov 25 2021
%Y A135688 Cf. A004001, A174232.
%K A135688 nonn
%O A135688 1,3
%A A135688 _Roger L. Bagula_, Feb 19 2008
%E A135688 Edited and corrected by _Eric M. Schmidt_, Dec 21 2014