cp's OEIS Frontend

A141435 a(1) = 1, a(2) = 2; a(n) = a(n-a(1)) + a(n-a(2)) + a(n-a(3)) + a(n-a(4)) + ...

%I A141435 #14 Jun 19 2019 11:11:20
%S A141435 1,2,3,6,11,20,38,71,132,247,461,861,1609,3005,5613,10485,19584,36581,
%T A141435 68330,127632,238404,445314,831798,1553712,2902170,5420945,10125754,
%U A141435 18913838,35329048,65990929,123264078,230244265,430071949,803328933
%N A141435 a(1) = 1, a(2) = 2; a(n) = a(n-a(1)) + a(n-a(2)) + a(n-a(3)) + a(n-a(4)) + ...
%C A141435 Thus we get a self-reference sequence that grows exponentially. a(n) = a(n-1) + a(n-2) + a(n-3) + a(n-6) + a(n-11) + a(n-20) + ...
%C A141435 A Fibonacci-like sequence, even closer to the tribonacci numbers.
%C A141435 Lim n-> oo log (a(n))/n converges.
%e A141435 a(6) = 20 because 20 = a(5) + a(4) + a(3) = 11 + 6 + 3
%e A141435 a(8) = 71 because 71 = a(7) + a(6) + a(5) + a(2) = 38 + 20 + 11 + 2
%p A141435 A141435 := proc(n) option remember; local a,i; if n <= 3 then RETURN(n); else a :=0 ; for i from 1 to n-1 do if n-procname(i) < 1 then RETURN(a); else a := a+procname(n-procname(i)) ; fi; od; RETURN(a); fi; end: for n from 1 to 80 do printf("%d,",A141435(n)) ; od: # _R. J. Mathar_, Nov 03 2008
%o A141435 (Python)
%o A141435 def A141435(terms):
%o A141435     seq = [1, 2]
%o A141435     for n in range(3, terms):
%o A141435         s = 0
%o A141435         for m in seq:
%o A141435             if (n - m) > 0:
%o A141435                 s += seq[n - m - 1] #fix for python indexing
%o A141435         seq.append(s)
%o A141435     return seq
%o A141435 print(A141435(40)) # _Andres Cruz y Corro A_, Jun 19 2019
%Y A141435 Cf. A058265, A008937, A001590, A000213, A000073, A096436, A102575, A111129.
%K A141435 easy,nonn
%O A141435 1,2
%A A141435 Raes Tom (tommy1729(AT)hotmail.com), Aug 06 2008
%E A141435 More terms from _R. J. Mathar_, Nov 03 2008