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

0,1

Comments

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

Links

Table of n, a(n) for n=0..48.

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)

Crossrefs

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

Sequence in context: A160172 A256536 A026412 * A301197 A008021 A228186

Adjacent sequences: A101421 A101422 A101423 * A101425 A101426 A101427

Keyword

nonn

Author

Anthony C Robin, Jan 17 2005

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

Status

approved