A131225 Triangle read by rows: T(n,k) = 2*k - (1 + (-1)^(n-k))/2 (1 <= k <= n).

1, 2, 3, 1, 4, 5, 2, 3, 6, 7, 1, 4, 5, 8, 9, 2, 3, 6, 7, 10, 11, 1, 4, 5, 8, 9, 12, 13, 2, 3, 6, 7, 10, 11, 14, 15, 1, 4, 5, 8, 9, 12, 13, 16, 17, 2, 3, 6, 7, 10, 11, 14, 15, 18, 19, 1, 4, 5, 8, 9, 12, 13, 16, 17, 20, 21, 2, 3, 6, 7, 10, 11, 14, 15, 18, 19, 22, 23

Offset: 1

Author

Gary W. Adamson, Jun 20 2007

Keywords

• nonn
• tabl

Comments

Row sums = A035608: (1, 5, 10, 18, 27, 39, ...).

Examples

			First few rows of the triangle:
  1;
  2,  3;
  1,  4,  5;
  2,  3,  6,  7;
  1,  4,  5,  8,  9;
  2,  3,  6,  7, 10, 11;
  1,  4,  5,  8,  9, 12, 13;
  ...
		

Crossrefs

Cf. A002260, A035608, A128174.

Programs

Maple

T := proc (n, k) options operator, arrow; 2*k-1/2-(1/2)*(-1)^(n-k) end proc: for n to 10 do seq(T(n, k), k = 1 .. n) end do; # yields sequence in triangular form - Emeric Deutsch, Jul 09 2007

Mathematica

T[n_,k_]:=2k-(1+(-1)^(n-k))/2;Table[T[n,k],{n,12},{k,n}]//Flatten (* James C. McMahon, Feb 17 2025 *)

Formula

2*A002260 - A128174, as infinite lower triangular matrices; where A002260 = (1; 1,2; 1,2,3; ...) and A128174 = (1; 0,1; 1,0,1; ...).

Extensions

a(47), a(49) corrected and more terms from Georg Fischer, Jun 07 2023