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).

0, 1, 1, 1, 2, 3, 4, 6, 9, 13, 19, 28, 32, 42, 52, 57, 63, 70, 82, 91, 98, 108, 118, 135, 144, 154, 163, 172, 182, 192, 202, 213, 225, 229, 235, 244, 257, 267, 277, 291, 306, 322, 334, 343, 350, 360, 370, 378, 387, 397, 415, 433, 452, 462, 472, 483, 495, 508, 523, 541, 554, 564, 574

Offset: 0

Author

Bob Selcoe, Nov 17 2014

Keywords

• nonn
• base
• easy

Examples

			a(10) = 28 because (0+1+1+2+3+5+8+1+3+2+1) + 1 = 28.
		

Links

• Michael De Vlieger, Table of n, a(n) for n = 0..2000

Crossrefs

Cf. A007953, A219675, A244510.

Programs

Maple

A247083 := proc(n)
    option remember;
    if n <= 0 then
        0;
    else
        1+add(digsum(procname(i)),i=0..n-3) ;
    end if;
end proc: # R. J. Mathar, Dec 02 2014

Mathematica

a247083[n_Integer] := Module[{t = Table[1, {i, n + 1}], j, k},
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 *)

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

Sage

n=100
a=[0,1,1]
for i in [3..n]:
    a.append(1+sum(sum(a[j].digits()) for j in [1..(i-3)]))
a # Tom Edgar, Nov 25 2014

Formula

a(n) = 1 + Sum_{k=0..n-3} digsum(a(k)).

a(n) = a(n-1) + A007953(a(n-3)).