A351153 Triangle read by rows: T(n, k) = n*(k - 1) - k*(k - 3)/2 with 0 < k <= n.

1, 1, 3, 1, 4, 6, 1, 5, 8, 10, 1, 6, 10, 13, 15, 1, 7, 12, 16, 19, 21, 1, 8, 14, 19, 23, 26, 28, 1, 9, 16, 22, 27, 31, 34, 36, 1, 10, 18, 25, 31, 36, 40, 43, 45, 1, 11, 20, 28, 35, 41, 46, 50, 53, 55, 1, 12, 22, 31, 39, 46, 52, 57, 61, 64, 66, 1, 13, 24, 34, 43, 51, 58, 64, 69, 73, 76, 78

Offset

1,3

Comments

Except for the number 2, it contains all the positive integers.

Links

Table of n, a(n) for n=1..78.

Formula

T(n, k) = 1 + Sum_{i=1..k-1} (n - i + 1).

From R. J. Mathar, Feb 07 2022: (Start)

G.f.: x*y*(1 - x + y*x^2 + y^2*x^3)/((1 - x)^2*(1 - y*x)^3).

T(n, k) = 1 + A141418(n+1, k-1) = 1 + A087401(n+1, k-1). (End)

Example

Triangle begins:
  1;
  1, 3;
  1, 4,  6;
  1, 5,  8, 10;
  1, 6, 10, 13, 15;
  1, 7, 12, 16, 19, 21;
  1, 8, 14, 19, 23, 26, 28;
  ...

Mathematica

Flatten[Table[n(k-1)-k(k-3)/2, {n, 12}, {k, n}]]

Crossrefs

Cf. A000012 (1st column), A000217 (leading diagonal), A005843 (3rd column), A006007 (sum of the first n rows), A006527 (row sums).

Cf. A087401, A141418, A351154.

Sequence in context: A286159 A307394 A194540 * A193043 A086271 A345229

Adjacent sequences: A351150 A351151 A351152 * A351154 A351155 A351156

Keyword

nonn,easy,tabl

Author

Stefano Spezia, Feb 02 2022

Status

approved