A129372 Triangle read by rows: T(n,k) = 1 if k divides n and n/k is odd, T(n,k) = 0 otherwise.

1, 0, 1, 1, 0, 1, 0, 0, 0, 1, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1

Offset: 1

Author

Gary W. Adamson, Apr 11 2007

Keywords

• nonn
• tabl

Examples

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

Links

• Andrew Howroyd, Table of n, a(n) for n = 1..1275

Crossrefs

Cf. A051731, A115359, A183063.

Cf. A001227 (row sums).

Programs

Magma

A129372:= func< n,k | (n mod k) eq 0 and (Floor(n/k) mod 2) eq 1 select 1 else 0 >;
[A129372(n,k): k in [1..n], n in [1..15]]; // G. C. Greubel, Feb 01 2024

Mathematica

A129372[n_, k_]:= If[Mod[n,k]==0 && OddQ[n/k], 1, 0];
Table[A129372[n, k], {n,15}, {k,n}]//Flatten (* G. C. Greubel, Feb 01 2024 *)

PARI

T(n,k)=if(n%k, 0, n/k%2==1) \\ Andrew Howroyd, Aug 10 2018

SageMath

def A129372(n,k): return 1 if (n%k)==0 and ((n/k)%2)==1 else 0
flatten([[A129372(n,k) for k in range(1,n+1)] for n in range(1,16)]) # G. C. Greubel, Feb 01 2024

Formula

Equals A051731 * A115359.

Sum_{k=1..n} T(n, k) = A001227(n) (row sums).

From G. C. Greubel, Feb 01 2024: (Start)

Sum_{k=1..n} (-1)^(k-1)*T(n, k) = (-1)^(n-1)*A001227(n).

Sum_{k=1..floor((n+1)/2)} T(n-k+1, k) = A183063(n+1). (End)

Extensions

Name changed and terms a(56) and beyond from Andrew Howroyd, Aug 10 2018