A199922 Table read by rows, T(0,0) = 1 and for n>0, 0<=k<=3^(n-1) T(n,k) = gcd(k,3^(n-1)).

1, 1, 1, 3, 1, 1, 3, 9, 1, 1, 3, 1, 1, 3, 1, 1, 9, 27, 1, 1, 3, 1, 1, 3, 1, 1, 9, 1, 1, 3, 1, 1, 3, 1, 1, 9, 1, 1, 3, 1, 1, 3, 1, 1, 27, 81, 1, 1, 3, 1, 1, 3, 1, 1, 9, 1, 1, 3, 1, 1, 3, 1, 1, 9, 1, 1, 3, 1, 1, 3, 1, 1, 27, 1, 1, 3, 1, 1, 3, 1, 1, 9, 1, 1, 3, 1, 1, 3, 1, 1, 9, 1, 1, 3, 1, 1, 3, 1, 1, 27, 1, 1, 3, 1, 1, 3, 1, 1, 9, 1, 1, 3, 1, 1, 3, 1, 1, 9, 1, 1, 3, 1, 1, 3, 1, 1, 81

Offset: 0

Author

Peter Luschny, Nov 12 2011

Keywords

• nonn
• tabf

Examples

			             1
            1, 1
         3, 1, 1, 3
9, 1, 1, 3, 1, 1, 3, 1, 1, 9
		

Links

• G. C. Greubel, Rows n = 0..8 of the irregular triangle, flattened

Crossrefs

Cf. A000007, A198069, A199923.

Programs

Magma

[1] cat [Gcd(k, 3^(n-1)): k in [0..3^(n-1)], n in [1..6]]; // G. C. Greubel, Nov 24 2023

Maple

seq(print(seq(gcd(k,3^(n-1)), k=0..3^(n-1))),n=0..4);

Mathematica

T[n_, k_]:= If[n==0, 1, GCD[k, 3^(n-1)]];
Table[T[n, k], {n,0,6}, {k,0,3^(n-1)}]//Flatten (* G. C. Greubel, Nov 24 2023 *)

SageMath

def A199922(n,k): return gcd(k, 3^(n-1)) + (2/3)*int(n==0)
flatten([[A199922(n,k) for k in range(int(3^(n-1))+1)] for n in range(7)]) # G. C. Greubel, Nov 24 2023

Formula

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

T(n, 3^(n-1) - k) = T(n, k).

Sum_{k=0..3^(n-1)} T(n, k) = A199923(n).

Sum_{k=0..3^(n-1)} (-1)^k * T(n, k) = A000007(n). (End)