A201385 Irregular triangle T(n,k) (n >= 1, k >= 1) read by rows: T(n,1) = 2^n - 1; for k>1, T(n,k) = 0 for n <= 2*(k-1); otherwise T(n+1,k) = T(n,k-1) + T(n,k).

1, 3, 7, 3, 15, 10, 31, 25, 10, 63, 56, 35, 127, 119, 91, 35, 255, 246, 210, 126, 511, 501, 456, 336, 126, 1023, 1012, 957, 792, 462, 2047, 2035, 1969, 1749, 1254, 462, 4095, 4082, 4004, 3718, 3003, 1716, 8191, 8177, 8086, 7722, 6721, 4719, 1716

Offset: 1

Author

Jonathan Vos Post, Nov 30 2011

Keywords

• nonn
• tabf
• easy

Comments

A "Pascal Staircase".

The zero entries simplify the definition, but are not part of the official triangle.

Examples

			Triangle begins:
    1
    3
    7   3
   15  10
   31  25 10
   63  56 35
  127 119 91 35
  ...
		

Links

• Alois P. Heinz, Rows n = 1..200, flattened
• Ozer Ozturk and Piotr Pragacz, On Schur function expansions of Thom polynomials, arXiv:1111.6612 [math.AG], 2011-2012. See (59), p. 22.

Crossrefs

Columns k = 1, 2, 3 give A000225, A000247, A272352(n+1).

Row sums give A130783.

Programs

Mathematica

With[{rowmax=20},DeleteCases[Transpose[PadLeft[NestWhileList[Accumulate[#[[2;;-2]]]&,2^Range[rowmax]-1,Length[#]>2&]]],0,2]] (* Paolo Xausa, Nov 07 2023 *)

Extensions

Entry revised by N. J. A. Sloane, Nov 07 2023