A372901 Numbers k that divide the k-th central Delannoy number.

1, 3, 9, 21, 27, 81, 171, 189, 217, 243, 297, 351, 729, 903, 1547, 2187, 3591, 3661, 4131, 5499, 5967, 6019, 6561, 7533, 8001, 11997, 13203, 14217, 15309, 17181, 19683, 20601, 22113, 22599, 23529, 24297, 25659, 26163, 26319, 26487, 28441, 30051, 33021, 37179, 37791

Offset

1,2

Comments

Numbers k such that k | A001850(k).

Links

Amiram Eldar, Table of n, a(n) for n = 1..307

Example

3 is a term since A001850(3) = 63 = 3 * 21 is divisible by 3.
9 is a term since A001850(9) = 1462563 = 9 * 162507 is divisible by 9.

Mathematica

Select[Range[1000], Divisible[LegendreP[#, 3], #] &]

Prog

(PARI) lista(kmax) = {my(cd0 = 1, cd1 = 3, cd2); print1("1, "); for(k = 2, kmax, cd2 = (3*(2*k-1)*cd1 - (k-1)*cd0)/k; if(!(cd2 % k), print1(k, ", ")); cd0 = cd1; cd1 = cd2); }

Crossrefs

Cf. A001850.

Similar sequences: A014847 (Catalan), A016089 (Lucas), A023172 (Fibonacci), A051177 (partition), A232570 (tribonacci), A246692 (Pell), A266969 (Motzkin).

Sequence in context: A045590 A369768 A242740 * A029536 A331131 A089322

Adjacent sequences: A372898 A372899 A372900 * A372902 A372903 A372904

Keyword

nonn

Author

Amiram Eldar, May 16 2024

Status

approved