A166692 Triangle T(n,k) read by rows: T(n,k) = 2^(k-1), k>0, T(n,0) = (n+1) mod 2.

1, 0, 1, 1, 1, 2, 0, 1, 2, 4, 1, 1, 2, 4, 8, 0, 1, 2, 4, 8, 16, 1, 1, 2, 4, 8, 16, 32, 0, 1, 2, 4, 8, 16, 32, 64, 1, 1, 2, 4, 8, 16, 32, 64, 128, 0, 1, 2, 4, 8, 16, 32, 64, 128, 256, 1, 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 0, 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024

Offset: 0

Author

Paul Curtz, Oct 18 2009

Keywords

• nonn
• easy
• tabl

Comments

Variant of A166918.

Examples

			Triangle begins as:
  1;
  0, 1;
  1, 1, 2;
  0, 1, 2, 4;
  1, 1, 2, 4, 8;
  0, 1, 2, 4, 8, 16;
		

Links

• G. C. Greubel, Rows n = 0..100 of the triangle, flattened

Crossrefs

Cf. A005578, A011782, A051049, A131577, A106624, A166494, A166918.

Programs

Magma

A166692:= func< n,k | k eq 0 select ((n+1) mod 2) else 2^(k-1) >;
[A166692(n,k): k in [0..n], n in [0..15]]; // G. C. Greubel, Apr 24 2023

Mathematica

Join[{1,0},Flatten[Riffle[Table[2^Range[0,n],{n,0,10}],{1,0}]]] (* Harvey P. Dale, Jan 18 2015 *)

SageMath

def A166692(n,k): return ((n+1)%2) if (k==0) else 2^(k-1)
flatten([[A166692(n,k) for k in range(n+1)] for n in range(16)]) # G. C. Greubel, Apr 24 2023

Formula

T(2n, k) = A011782(k).

T(2n+1, k) = A131577(k).

Sum_{k=0..n} T(n,k) = A051049(n).

From G. C. Greubel, Apr 24 2023: (Start)

T(2*n, n) = A011782(n).

Sum_{k=0..n} (-1)^k*T(n, k) = (-1)^n * A005578(n).

Sum_{k=0..n} T(n-k, k) = A106624(n). (End)

Extensions

More terms from Harvey P. Dale, Jan 18 2015