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

1,2

Links

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

Example

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

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 *)

Crossrefs

Cf. A081927, A081928.

Sequence in context: A087712 A180702 A263328 * A242614 A069800 A275536

Adjacent sequences: A081923 A081924 A081925 * A081927 A081928 A081929

Keyword

base,easy,nonn,tabl,look

Author

Amarnath Murthy, Apr 01 2003

Status

approved