A099233 Square array read by antidiagonals associated to sections of 1/(1-x-x^k).

1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 3, 3, 1, 1, 1, 4, 6, 5, 1, 1, 1, 5, 10, 13, 8, 1, 1, 1, 6, 15, 26, 28, 13, 1, 1, 1, 7, 21, 45, 69, 60, 21, 1, 1, 1, 8, 28, 71, 140, 181, 129, 34, 1, 1, 1, 9, 36, 105, 251, 431, 476, 277, 55, 1, 1, 1, 10, 45, 148, 413, 882, 1326, 1252, 595, 89, 1

Offset: 0

Author

Paul Barry, Oct 08 2004

Keywords

• easy
• nonn
• tabl

Examples

			Rows begin
  1, 1, 1,  1,  1,   1, ...
  1, 1, 2,  3,  5,   8, ...
  1, 1, 3,  6, 13,  28, ...
  1, 1, 4, 10, 26,  69, ...
  1, 1, 5, 15, 45, 140, ...
Row 1 is the 0-section of 1/(1-x-x)   (A000079);
Row 2 is the 1-section of 1/(1-x-x^2) (A000045);
Row 3 is the 2-section of 1/(1-x-x^3) (A000930);
Row 4 is the 3-section of 1/(1-x-x^4) (A003269);
etc.
		

Links

• Seiichi Manyama, Antidiagonals n = 0..139, flattened

Crossrefs

Sums of antidiagonals are A099236.

Columns include A000217, A008778.

Rows include A000045, A002478, A099234, A099235.

Main diagonal gives A099237.

Cf. A099238.

Formula

Square array T(n, k) = Sum_{j=0..n} binomial(k(n-j), j).

Rows are generated by 1/(1-x(1+x)^k) and satisfy a(n) = Sum_{k=0..n} binomial(n, k)a(n-k-1).