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a(n) = A004001(n)*a(n-1) + a(n-2), for n > 2, with a(1) = a(2) = 1.
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%I #16 May 16 2022 11:02:23

%S 1,1,3,7,24,103,436,1847,9671,59873,428782,3061347,24919558,202417811,

%T 1644262046,13356514179,121852889657,1231885410749,13672592407896,

%U 165302994305501,1997308524073908,26130313807266305,367821701825802178

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

%H G. C. Greubel, <a href="/A135688/b135688.txt">Table of n, a(n) for n = 1..500</a>

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

%t HC[n_]:= HC[n]= If[n<3, Fibonacci[n], HC[HC[n-1]] +HC[n -HC[n-1]]]; (*A004001*)

%t a[n_] := a[n] = If[n<3, 1, HC[n]*a[n-1] + a[n-2]];

%t Table[a[n], {n, 40}]

%o (Sage)

%o @cached_function

%o def HC(n): # HC = A004001

%o if (n<3): return fibonacci(n)

%o else: return HC(HC(n-1)) +HC(n -HC(n-1))

%o @CachedFunction

%o def a(n): # A135688

%o if (n<3): return 1

%o else: return HC(n)*a(n-1) + a(n-2)

%o [a(n) for n in (1..40)] # _G. C. Greubel_, Nov 25 2021

%Y Cf. A004001, A174232.

%K nonn

%O 1,3

%A _Roger L. Bagula_, Feb 19 2008

%E Edited and corrected by _Eric M. Schmidt_, Dec 21 2014