A101425 Number of different cuboids with volume p^5 X q^n, where p,q are distinct prime numbers.

5, 12, 24, 38, 57, 78, 104, 132, 165, 200, 240, 282, 329, 378, 432, 488, 549, 612, 680, 750, 825, 902, 984, 1068, 1157, 1248, 1344, 1442, 1545, 1650, 1760, 1872, 1989, 2108, 2232, 2358, 2489, 2622, 2760, 2900, 3045, 3192, 3344, 3498, 3657, 3818, 3984, 4152

Offset

0,1

Comments

Subsequence of A034836, which gives the number of cuboids for volume n.

Links

Table of n, a(n) for n=0..47.

Formula

a(n) = A034836(2^5*3^n) = A034836(3^5*2^n) = A034836(p^5*q^n) for p,q distinct primes.

From Colin Barker, Mar 28 2014: (Start)

The following is conjectured.

a(n) = (37+3*(-1)^n+48*n+14*n^2)/8.

a(n) = 2*a(n-1)-2*a(n-3)+a(n-4).

G.f.: -(2*x+5)/((x+1)*(x-1)^3). (End)

a(n) = 7*(n+2)*(n+1)/4 + 3*(floor(n/2)+1)/2. - Chai Wah Wu, May 28 2026

Prog

(Python)
def A101425(n): return ((7*(n+2)*(n+1)>>1)+3*((n>>1)+1))>>1 # Chai Wah Wu, May 28 2026

Crossrefs

Cf. A034836, A101423, A101424, A101426, A101427.

Sequence in context: A344510 A100479 A018806 * A394229 A191831 A365540

Adjacent sequences: A101422 A101423 A101424 * A101426 A101427 A101428

Keyword

nonn,changed

Author

Anthony C Robin, Jan 17 2005

Extensions

Edited and extended by Ray Chandler, Dec 19 2008

a(0)=5 prepended and g.f. edited by Alois P. Heinz, Oct 05 2016

Status

approved