A067574 Array T(i,j) read by ascending antidiagonals, where T(i,j) is the concatenation of i and j (1<=i, 1<=j).

11, 21, 12, 31, 22, 13, 41, 32, 23, 14, 51, 42, 33, 24, 15, 61, 52, 43, 34, 25, 16, 71, 62, 53, 44, 35, 26, 17, 81, 72, 63, 54, 45, 36, 27, 18, 91, 82, 73, 64, 55, 46, 37, 28, 19, 101, 92, 83, 74, 65, 56, 47, 38, 29, 110, 111, 102, 93, 84, 75, 66, 57, 48, 39, 210, 111

Offset: 1

Author

Robert G. Wilson v, Jan 30 2002

Keywords

• base
• easy
• nonn
• tabl

Comments

The antidiagonals are read in the opposite direction to those in A066686.

Examples

			The array begins
11 12 13 14 15 16 17 18 19 110 ...
21 22 23 24 25 26 27 28 29 210 ...
31 32 33 34 35 36 37 38 39 310 ...
41 42 43 44 45 46 47 48 49 410 ...
		

Crossrefs

Cf. A055642, A066686, A084854.

Programs

Mathematica

a = {}; Do[ a = Append[a, ToExpression[ StringJoin[ ToString[i - j], ToString[j]]]], {i, 2, 13}, {j, 1, i - 1} ]; a

Python

def T(i, j): return int(str(i) + str(j))
def auptodiag(maxd):
    return [T(d+1-j, j) for d in range(1, maxd+1) for j in range(1, d+1)]
print(auptodiag(12)) # Michael S. Branicky, Nov 21 2021

Formula

T(i, j) = i*10^A055642(i) + j. - Michael S. Branicky, Nov 21 2021