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a(n)=0 when n<=0: Starting with n=1, a(n) = 1 + the sum of the digital sums of a(0) through a(n-4).
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%I #28 Jan 02 2023 12:30:50

%S 0,1,1,1,1,2,3,4,5,7,10,14,19,26,27,32,42,50,59,64,70,75,89,99,106,

%T 118,135,153,160,170,179,188,195,203,220,237,252,257,261,273,282,296,

%U 305,317,329,346,354,365,379,392,404,418,437,451,459,472,486,496,514

%N a(n)=0 when n<=0: Starting with n=1, a(n) = 1 + the sum of the digital sums of a(0) through a(n-4).

%H Eric Angelini, <a href="http://list.seqfan.eu/oldermail/seqfan/2014-November/013951.html">a(n) > cumulative sum of digits</a>, Seqfan, Nov. 11, 2014.

%F a(n) = 1 + Sum_{k=0..n-4} digsum(a(k)).

%F a(n) = a(n-1) + digsum(a(n-4)).

%e a(15) = 32 because (0+1+1+1+1+2+3+4+5+7+1+0+1+4) + 1 = 32.

%t a247084[n_Integer] := Module[{t = Table[1, {i, n + 1}], j, k},

%t t[[1]] = 0; j = 6; While[j <= Length[t], t[[j]] = Sum[Plus @@ IntegerDigits[t[[k]]], {k, 1, j - 4}]; ++]; Drop[t, {2}]]; a247084[59] (* _Michael De Vlieger_, Nov 29 2014 *)

%o (PARI) lista(nn) = {v = vector(nn); for (n=2, nn, v[n] = 1 + sum(i=1, n-4, if (n-4 > 0, sumdigits(v[i])));); v;} \\ _Michel Marcus_, Nov 18 2014

%Y Cf. A007953, A219675, A244510 (related).

%K base,nonn

%O 0,6

%A _Bob Selcoe_, Nov 17 2014

%E More terms from _Michel Marcus_, Nov 18 2014