A358360 The 3-adic valuation of the central Delannoy numbers (sequence A001850).

0, 1, 0, 2, 1, 2, 0, 1, 0, 3, 2, 3, 1, 2, 1, 3, 2, 3, 0, 1, 0, 2, 1, 2, 0, 1, 0, 4, 3, 4, 2, 3, 2, 4, 3, 4, 1, 2, 1, 3, 2, 3, 1, 2, 1, 4, 3, 4, 2, 3, 2, 4, 3, 4, 0, 1, 0, 2, 1, 2, 0, 1, 0, 3, 2, 3, 1, 2, 1, 3, 2, 3, 0, 1, 0, 2, 1, 2, 0, 1, 0, 5, 4, 5, 3, 4, 3

Offset: 0

Author

Jeffrey Shallit, Nov 12 2022

Keywords

• nonn

Comments

The 3-adic valuation of x is the exponent of the highest power of 3 dividing x.

References

• J.-P. Allouche and J. Shallit, Automatic Sequences: Theory, Applications, Generalizations. Cambridge University Press (2003), p. 453.

Links

• J. Shallit, k-regular sequences. Talk for the Colloque Michel Mendès France, Bordeaux, France, December 12 2000.
• Zhao Shen, On a conjecture of J. Shallit about Apéry-like numbers, arXiv:2112.11135 [math.NT], January 2 2022.

Crossrefs

Cf. A001850, A007949.

Programs

Mathematica

Array[IntegerExponent[LegendreP[#, 3], 3] &, 105, 0] (* Michael De Vlieger, Nov 12 2022 *)

Formula

b(n) = b(floor(n/3)) + (floor(n/3) mod 2), if n == 0,2 (mod 3);

b(n) = b(floor(n/9)) + 1, if n == 1 (mod 3).

a(n) = A007949(A001850(n)).