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A296440 a(1) = 2, a(2) = a(3) = 3, a(4) = 4, a(5) = a(6) = 6; a(n) = a(n-a(n-1)) + a(n-a(n-2)) + a(n-a(n-3)) for n > 6.

%I A296440 #27 Jan 27 2025 21:11:45
%S A296440 2,3,3,4,6,6,7,8,8,9,9,10,11,13,13,12,14,16,16,14,19,17,18,19,21,21,
%T A296440 20,22,23,24,23,24,25,26,26,27,27,28,29,30,30,31,32,34,33,34,35,37,36,
%U A296440 37,39,36,39,42,39,41,41,44,45,41,40,50,46,48,43,48,51,49,49,54,48,53,51,58,50,58,52,57,56,59,57,60,58
%N A296440 a(1) = 2, a(2) = a(3) = 3, a(4) = 4, a(5) = a(6) = 6; a(n) = a(n-a(n-1)) + a(n-a(n-2)) + a(n-a(n-3))  for n > 6.
%C A296440 Conjecture: Sequence is infinite.
%H A296440 Altug Alkan, <a href="/A296440/b296440.txt">Table of n, a(n) for n = 1..10000</a>
%H A296440 Altug Alkan, <a href="/A296440/a296440.png">Scatterplot of a(n)-2*n/3</a>
%H A296440 Hans Havermann, <a href="/A296440/a296440_1.png">Scatterplot of a(n) for n <= 10^7</a>
%p A296440 a:= proc(n) option remember; procname(n-procname(n-1))+procname(n-procname(n-2))+procname(n-procname(n-3)) end proc:
%p A296440 a(1):= 2: a(2):= 3: a(3):= 3: a(4):= 4: a(5):= 6: a(6):= 6:
%p A296440 map(a, [$1..100]); # _Robert Israel_, Dec 12 2017
%t A296440 a[n_] := a[n] = If[n<7, {2, 3, 3, 4, 6, 6}[[n]], a[n - a[n-1]] + a[n - a[n-2]] + a[n - a[n-3]]]; Array[a, 83] (* _Giovanni Resta_, Dec 13 2017 *)
%o A296440 (PARI) my(q=vector(100)); q[1]=2;q[2]=3;q[3]=3;q[4]=4;q[5]=6;q[6]=6; for(n=7, #q, q[n] = q[n-q[n-1]]+q[n-q[n-2]]+q[n-q[n-3]]); q
%o A296440 (Scheme)
%o A296440 ;; With memoization-macro definec.
%o A296440 (definec (A296440 n) (cond ((= 1 n) 2) ((<= n 3) 3) ((= 4 n) 4) ((<= n 6) 6) (else (+ (A296440 (- n (A296440 (- n 1)))) (A296440 (- n (A296440 (- n 2)))) (A296440 (- n (A296440 (- n 3)))))))) ;; _Antti Karttunen_, Dec 13 2017
%Y A296440 Cf. A005185, A278055, A284644, A292351.
%K A296440 nonn,look
%O A296440 1,1
%A A296440 _Altug Alkan_, Dec 12 2017