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A247083 a(n) = 0 for n <= 0: Starting with n=1, a(n) = 1 + the sum of the digital sums of a(0) through a(n-3).

%I A247083 #39 Mar 14 2020 16:59:09
%S A247083 0,1,1,1,2,3,4,6,9,13,19,28,32,42,52,57,63,70,82,91,98,108,118,135,
%T A247083 144,154,163,172,182,192,202,213,225,229,235,244,257,267,277,291,306,
%U A247083 322,334,343,350,360,370,378,387,397,415,433,452,462,472,483,495,508,523,541,554,564,574
%N A247083 a(n) = 0 for n <= 0: Starting with n=1, a(n) = 1 + the sum of the digital sums of a(0) through a(n-3).
%H A247083 Michael De Vlieger, <a href="/A247083/b247083.txt">Table of n, a(n) for n = 0..2000</a>
%F A247083 a(n) = 1 + Sum_{k=0..n-3} digsum(a(k)).
%F A247083 a(n) = a(n-1) + A007953(a(n-3)).
%e A247083 a(10) = 28 because (0+1+1+2+3+5+8+1+3+2+1) + 1 = 28.
%p A247083 A247083 := proc(n)
%p A247083     option remember;
%p A247083     if n <= 0 then
%p A247083         0;
%p A247083     else
%p A247083         1+add(digsum(procname(i)),i=0..n-3) ;
%p A247083     end if;
%p A247083 end proc: # _R. J. Mathar_, Dec 02 2014
%t A247083 a247083[n_Integer] := Module[{t = Table[1, {i, n + 1}], j, k},
%t A247083 t[[1]] = 0; j = 5; While[j <= Length[t], t[[j]] = Sum[Plus @@ IntegerDigits[t[[k]]], {k, 1, j - 3}]; j++]; Drop[t, {2}]]; a247083[63] (* _Michael De Vlieger_, Nov 26 2014 *)
%o A247083 (Sage)
%o A247083 n=100
%o A247083 a=[0,1,1]
%o A247083 for i in [3..n]:
%o A247083     a.append(1+sum(sum(a[j].digits()) for j in [1..(i-3)]))
%o A247083 a # _Tom Edgar_, Nov 25 2014
%o A247083 (PARI) v=[0];n=1;while(n<100,s=0;for(i=1,#v-2,s+=sumdigits(v[i]));v=concat(v,1+s);n++);v \\ _Derek Orr_, Nov 26 2014
%Y A247083 Cf. A007953, A219675, A244510.
%K A247083 nonn,base,easy
%O A247083 0,5
%A A247083 _Bob Selcoe_, Nov 17 2014