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A228297 Generalized meta-Fibonacci sequence a(n) with parameters s=0 and k=5.

%I A228297 #58 Dec 30 2023 23:56:58
%S A228297 1,2,3,4,5,5,6,7,8,9,10,10,11,12,13,14,15,15,16,17,18,19,20,20,21,22,
%T A228297 23,24,25,25,25,26,27,28,29,30,30,31,32,33,34,35,35,36,37,38,39,40,40,
%U A228297 41,42,43,44,45,45,46,47,48,49,50,50,50,51,52,53
%N A228297 Generalized meta-Fibonacci sequence a(n) with parameters s=0 and k=5.
%C A228297 Each integer n appears x+1 times where x is the greatest power of 5 in the factorization of n!. - _Gerald Hillier_, Feb 08 2020
%H A228297 Michael De Vlieger, <a href="/A228297/b228297.txt">Table of n, a(n) for n = 1..10000</a>
%H A228297 C. Deugau and F. Ruskey, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL12/Ruskey/ruskey6.html">Complete k-ary Trees and Generalized Meta-Fibonacci Sequences</a>, J. Integer Seq., Vol. 12, 2009, Article 09.4.3.
%F A228297 a(n) = A007845(n)/5. - _M. F. Hasler_, Dec 27 2019
%t A228297 Array[ConstantArray[#, IntegerExponent[#, 5] + 1] &, 53] // Flatten (* _Michael De Vlieger_, Feb 08 2020 *)
%o A228297 (PARI) a(n)= {local(A); if(n<=5, max(0, n), A=vector(n, i, i); for(k=6, n, A[k]= A[k-A[k-1]] + A[k-1-A[k-2]] + A[k-2-A[k-3]] + A[k-3-A[k-4]] + A[k-4-A[k-5]];); A[n];);}
%o A228297 (HP 49G calculator)
%o A228297 « DUPDUP 5 IQUOT -
%o A228297   WHILE DUP 0 OVER
%o A228297     DO 5 IQUOT DUP
%o A228297 ROT + SWAP DUP NOT
%o A228297     UNTIL
%o A228297     END DROP +
%o A228297 PICK3 <
%o A228297   REPEAT 1 +
%o A228297   END NIP
%o A228297 » _Gerald Hillier_, Sep 19 2017
%Y A228297 Cf. A120503, A120507, A228298.
%K A228297 nonn
%O A228297 1,2
%A A228297 _Michel Marcus_, Aug 20 2013