A081926 Triangle read by rows in which n-th row gives n smallest numbers with digit sum n.

1, 2, 11, 3, 12, 21, 4, 13, 22, 31, 5, 14, 23, 32, 41, 6, 15, 24, 33, 42, 51, 7, 16, 25, 34, 43, 52, 61, 8, 17, 26, 35, 44, 53, 62, 71, 9, 18, 27, 36, 45, 54, 63, 72, 81, 19, 28, 37, 46, 55, 64, 73, 82, 91, 109, 29, 38, 47, 56, 65, 74, 83, 92, 119, 128, 137

Offset: 1

Author

Amarnath Murthy, Apr 01 2003

Keywords

• base
• easy
• nonn
• tabl
• look

Examples

			Triangle starts
1
2 11
3 12 21
4 13 22 31
5 14 23 32 41
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10011 (first 141 rows, flattened; first 40 rows from T. D. Noe)

Crossrefs

Cf. A081927, A081928.

Programs

Maple

f:= proc(n) local Res, d, v, count;
    Res:= NULL; count:= 0;
    for d from ceil(n/9) while count < n do
       v:= g(n,d,n-count,1);
       Res:= Res, op(v);
       count:= count + nops(v);
    od:
    Res
end proc:
g:= proc(n,d,remain) local rem, Res, j, j0, v;
      if remain = 0 then return [] else rem:= remain fi;
      if nargs = 4 then j0:= 1 else j0:= 0 fi;
      if d = 1 then if n >= j0 and n <= 9 then [n] else [] fi
      else
        Res:= NULL;
        for j from max(j0, ceil(n-9*(d-1))) to min(9,n) while rem > 0 do
          v:= map(t -> j*10^(d-1)+t, procname(n-j,d-1,rem));
          Res:= Res, op(v);
          rem:= rem - nops(v);
        od;
        [Res]
      fi
end proc:
for i from 1 to 25 do f(i) od; # Robert Israel, Feb 19 2018

Mathematica

Needs["Combinatorica`"]; Table[Take[Union[Flatten[Table[FromDigits /@ Permutations[PadRight[s, 6]], {s, Partitions[n, 9]}]]], n], {n, 40}] (* T. D. Noe, Mar 08 2013 *)