A378068 Table read by row: T(n, k) = Sum_{j=0..k} A217831(n, j). Partial row sums of Euclid's triangle.

0, 1, 2, 0, 1, 1, 0, 1, 2, 2, 0, 1, 1, 2, 2, 0, 1, 2, 3, 4, 4, 0, 1, 1, 1, 1, 2, 2, 0, 1, 2, 3, 4, 5, 6, 6, 0, 1, 1, 2, 2, 3, 3, 4, 4, 0, 1, 2, 2, 3, 4, 4, 5, 6, 6, 0, 1, 1, 2, 2, 2, 2, 3, 3, 4, 4, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 10, 0, 1, 1, 1, 1, 2, 2, 3, 3, 3, 3, 4, 4

Offset: 0

Author

Peter Luschny, Dec 26 2024

Keywords

• nonn
• tabl

Examples

			Triangle starts:
   [0] [0]
   [1] [1, 2]
   [2] [0, 1, 1]
   [3] [0, 1, 2, 2]
   [4] [0, 1, 1, 2, 2]
   [5] [0, 1, 2, 3, 4, 4]
   [6] [0, 1, 1, 1, 1, 2, 2]
   [7] [0, 1, 2, 3, 4, 5, 6, 6]
   [8] [0, 1, 1, 2, 2, 3, 3, 4, 4]
   [9] [0, 1, 2, 2, 3, 4, 4, 5, 6, 6]
  [10] [0, 1, 1, 2, 2, 2, 2, 3, 3, 4, 4]
		

Crossrefs

Cf. A000010 (subdiagonal), A217831 (Euclid's triangle), A092790 (row sums)

Programs

Maple

aRow := n -> local k; ListTools:-PartialSums([seq(if NumberTheory:-AreCoprime(n, k) then 1 else 0 fi, k = 0..n)]): seq(print(aRow(n)), n = 0..10);

Mathematica

aRow[n_] := Accumulate[Table[If[CoprimeQ[n, k], 1, 0], {k, 0, n}]];
Table[aRow[n], {n, 0, 10}] // Flatten

Formula

Prepending [0, 3] and setting offset = 0 sequence A092790 becomes the row sums.