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

0,6

Comments

Variant of A166918.

Links

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

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)

Example

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

Mathematica

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

Prog

(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
(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

Crossrefs

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

Sequence in context: A361853 A144172 A227318 * A046766 A292147 A003285

Adjacent sequences: A166689 A166690 A166691 * A166693 A166694 A166695

Keyword

nonn,easy,tabl

Author

Paul Curtz, Oct 18 2009

Extensions

More terms from Harvey P. Dale, Jan 18 2015

Status

approved