A256493 Number of factorizations of m^3 into at most 3 factors, where m is a product of exactly n distinct primes.

1, 3, 19, 171, 1675, 16683, 166699, 1666731, 16666795, 166666923, 1666667179, 16666667691, 166666668715, 1666666670763, 16666666674859, 166666666683051, 1666666666699435, 16666666666732203, 166666666666797739, 1666666666666928811, 16666666666667190955

Offset

0,2

Comments

Also the number of n-partite partitions of (3)^n into at most 3 n-tuples.

Links

Alois P. Heinz, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (13,-32,20).

Formula

G.f.: -(12*x^2-10*x+1)/((x-1)*(2*x-1)*(10*x-1)).

a(n) = (10^n + 3*2^n + 2)/6.

Example

The a(1) = 3 factorizations of 2^3 into at most 3 factors are: 8, 2*4, 2*2*2.
The a(2) = 19 factorizations of (2*3)^3 into at most 3 factors are: 216, 2*108, 3*72, 4*54, 6*36, 8*27, 9*24, 12*18, 2*2*54, 2*3*36, 2*4*27, 2*6*18, 2*9*12, 3*3*24, 3*4*18, 3*6*12, 3*8*9, 4*6*9, 6*6*6.

Maple

a:= n-> (10^n + 3*2^n + 2)/6: seq(a(n), n=0..30);

Mathematica

LinearRecurrence[{13, -32, 20}, {1, 3, 19}, 30] (* Harvey P. Dale, Dec 30 2019 *)

Crossrefs

Row n=3 of A256384.

Sequence in context: A094956 A080894 A143768 * A353256 A275283 A349768

Adjacent sequences: A256490 A256491 A256492 * A256494 A256495 A256496

Keyword

nonn,easy

Author

Alois P. Heinz, Mar 30 2015

Status

approved