A101424 Number of different cuboids with volume p^4 * q^n, where p,q are distinct prime numbers.

4, 9, 18, 28, 42, 57, 76, 96, 120, 145, 174, 204, 238, 273, 312, 352, 396, 441, 490, 540, 594, 649, 708, 768, 832, 897, 966, 1036, 1110, 1185, 1264, 1344, 1428, 1513, 1602, 1692, 1786, 1881, 1980, 2080, 2184, 2289, 2398, 2508, 2622, 2737, 2856, 2976, 3100

Offset: 0

Author

Anthony C Robin, Jan 17 2005

Keywords

• nonn

Comments

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

Crossrefs

Cf. A034836, A101423, A101425, A101426, A101427.

Formula

a(n) = A034836(2^4*3^n) = A034836(3^4*2^n) = A034836(p^4*q^n) for p,q distinct primes.

From Colin Barker, Mar 28 2014: (Start)

The following is conjectured.

a(n) = (29 + 3*(-1)^n + 36*n + 10*n^2)/8.

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

G.f.: -(x+4)/((x+1)*(x-1)^3). (End)

Extensions

Edited and extended by Ray Chandler, Dec 19 2008

a(0)=4 prepended and g.f. edited by Alois P. Heinz, Oct 05 2016