A242614 Triangle read by rows: row n contains numbers with sum of digits = n, and not greater than the n-th repunit (cf. A007953 and A002275).

0, 1, 2, 11, 3, 12, 21, 30, 102, 111, 4, 13, 22, 31, 40, 103, 112, 121, 130, 202, 211, 220, 301, 310, 400, 1003, 1012, 1021, 1030, 1102, 1111, 5, 14, 23, 32, 41, 50, 104, 113, 122, 131, 140, 203, 212, 221, 230, 302, 311, 320, 401, 410, 500, 1004, 1013, 1022

Offset

0,3

Comments

Number of terms in row n = A242622(n);

T(n,1) = A051885(n);

T(n,A242622(n)) = A002275(n);

for n > 0: number of repdigit terms in row n = A242627(n).

Links

Reinhard Zumkeller, Rows n = 0..8 of table, flattened

Example

The triangle begins:
. 0:  0
. 1:  1
. 2:  2,11
. 3:  3,12,21,30,102,111
. 4:  4,13,22,31,40,103,112,121,130,202, . . . ,1021,1030,1102,1111
. 5:  5,14,23,32,41,50,104,113,122,131, . . . ,11021,11030,11102,11111 .

Mathematica

Join[{0}, Flatten[Table[Select[Range[FromDigits[PadRight[{}, n, 1]]], Total[ IntegerDigits[ #]] == n&], {n, 5}]]] (* Harvey P. Dale, Oct 08 2019 *)

Prog

(Haskell)
a242614 n k = a242614_row n !! (k-1)
a242614_row n = filter ((== n) . a007953) [n .. a002275 n]
a242614_tabf = map a242614_row [0..]

Crossrefs

Cf. A007953 (sum of digits), A002275 (repunits).

Cf. A011557, A052216, A052217, A052218, A052219, A052220, A052221, A052222, A052223, A052224, A166311, A235151, A143164, A235225, A235226, A235227, A166370, A235228, A166459, A235229.

Sequence in context: A180702 A263328 A081926 * A069800 A275536 A060002

Adjacent sequences: A242611 A242612 A242613 * A242615 A242616 A242617

Keyword

nonn,tabf,base

Author

Reinhard Zumkeller, Jul 16 2014

Status

approved