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

0,4

Links

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

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)

Example

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

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 *)

Prog

(Magma) [1] cat [Gcd(k, 3^(n-1)): k in [0..3^(n-1)], n in [1..6]]; // 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

Crossrefs

Cf. A000007, A198069, A199923.

Sequence in context: A132740 A106621 A011085 * A112508 A260883 A088749

Adjacent sequences: A199919 A199920 A199921 * A199923 A199924 A199925

Keyword

nonn,tabf

Author

Peter Luschny, Nov 12 2011

Status

approved