A153860 Triangle by columns: leftmost column = (1, 0, 1, -1, 1, -1, 1, ...); columns >1 = (1, 1, 0, 0, 0, ...).

1, 0, 1, 1, 1, 1, -1, 0, 1, 1, 1, 0, 0, 1, 1, -1, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 1, 1, -1, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 1, 1, -1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1

Offset: 1

Author

Gary W. Adamson, Jan 03 2009

Keywords

• tabl
• sign

Comments

As an infinite lower triangular matrix M; M * [1,2,3,...] = A063210: (1, 2, 6, 6, 10, 10, 14, 14, ...).

M * [1, 3, 5, 7, ...] = A047471, {1,3} mod 8.

Eigensequence of the triangle = A066983 starting (1, 1, 3, 3, 7, 9, 17, 25, ...).

Binomial transform of the triangle = A153861.

Row sums = A153284: (1, 1, 3, 1, 3, 1, 3, 1, ...).

Examples

			First few rows of the triangle:
   1;
   0, 1;
   1, 1, 1;
  -1, 0, 1, 1;
   1, 0, 0, 1, 1;
  -1, 0, 0, 0, 1, 1;
   1, 0, 0, 0, 0, 1, 1;
  -1, 0, 0, 0, 0, 0, 1, 1;
   1, 0, 0, 0, 0, 0, 0, 1, 1;
  ...
		

Links

• Reinhard Zumkeller, Rows n = 1..100 of triangle, flattened

Crossrefs

Cf. A153861 (binomial transform), A153284 (row sums), A063210, A047471, A066983.

Programs

Haskell

a153860 n k = a153860_tabl !! (n-1) !! (k-1)
a153860_row n = a153860_tabl !! (n-1)
a153860_tabl = [1] : [0, 1] : iterate (\(x:xs) -> -x : 0 : xs) [1, 1, 1]
-- Reinhard Zumkeller, Dec 16 2013

Formula

Triangle by columns: leftmost column = (1, 0, 1, -1, 1, ...); columns > 1 = (1, 1, 0, 0, 0, ...).