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

0,3

Links

Table of n, a(n) for n=0..90.

Formula

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

Example

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]

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

Crossrefs

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

Sequence in context: A101672 A083731 A374058 * A216266 A177416 A087606

Adjacent sequences: A378064 A378065 A378066 * A378069 A378070 A378071

Keyword

nonn,tabl,new

Author

Peter Luschny, Dec 26 2024

Status

approved