A129765 Triangle, (1, 1, 2, 2, 2, ...) in every column.

1, 1, 1, 2, 1, 1, 2, 2, 1, 1, 2, 2, 2, 1, 1, 2, 2, 2, 2, 1, 1, 2, 2, 2, 2, 2, 1, 1, 2, 2, 2, 2, 2, 2, 1, 1, 2, 2, 2, 2, 2, 2, 2, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1

Offset: 1

Author

Gary W. Adamson, May 16 2007

Keywords

• nonn
• tabl
• easy

Comments

Row sums = A004277, (1, 2, 4, 6, 8, 10, ...). Binomial transform of (1, 1, 2, 2, 2, ...) = A000325, starting (1, 2, 5, 12, 27, 58, ...). Binomial transform of A130196 = A130197, a triangle with row sums = the Cullen numbers, A002064.

Examples

			First few rows of the triangle:
  1;
  1, 1;
  2, 1, 1;
  2, 2, 1, 1;
  2, 2, 2, 1, 1;
  ...
		

Crossrefs

Cf. A004277, A002064, A000325, A130197.

Programs

Maple

A129765 := proc(n,m) if abs(n-m)<2 then 1 ; else 2 ; end if ; end proc:
for n from 1 to 18 do for m from 1 to n do printf("%d,", A129765(n,m)) ; od ; od ; # R. J. Mathar, Jun 08 2007

Mathematica

Table[PadLeft[{1,1},n,2],{n,20}]//Flatten (* Harvey P. Dale, May 20 2019 *)

Formula

Triangle, (1, 1, 2, 2, 2, ...) in every column. By rows, (1; 1, 1; 2, 1, 1; ...), continuing with (n-2) 2's followed by two 1's. Inverse of A000012 as an infinite lower triangular matrix (all 1's and the rest zeros), signed by columns: (+ - - + + - -, ...).

Extensions

More terms from R. J. Mathar, Jun 08 2007