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

1,4

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.

Links

Table of n, a(n) for n=1..105.

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: (+ - - + + - -, ...).

Example

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

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 *)

Crossrefs

Cf. A004277, A002064, A000325, A130197.

Sequence in context: A174886 A157415 A154325 * A143187 A348042 A143209

Adjacent sequences: A129762 A129763 A129764 * A129766 A129767 A129768

Keyword

nonn,tabl,easy

Author

Gary W. Adamson, May 16 2007

Extensions

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

Status

approved