A101426 Number of different cuboids with volume p^6 * q^n, where p,q are distinct prime numbers.

7, 16, 32, 51, 76, 104, 139, 176, 220, 267, 320, 376, 439, 504, 576, 651, 732, 816, 907, 1000, 1100, 1203, 1312, 1424, 1543, 1664, 1792, 1923, 2060, 2200, 2347, 2496, 2652, 2811, 2976, 3144, 3319, 3496, 3680, 3867, 4060, 4256, 4459, 4664, 4876, 5091, 5312

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..46.

Formula

a(n) = A034836(2^6*3^n) = A034836(3^6*2^n) = A034836(p^6*q^n) for p,q distinct primes.

Empirical g.f.: -(3*x^3+9*x^2+9*x+7)/((x+1)*(x^2+x+1)*(x-1)^3). - Colin Barker, Mar 28 2014

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

Prog

(Python)
def A101426(n): return (7*(n+2)*(n+1)+(0 if n%3 else 1))//3+(n&-2)+2 # Chai Wah Wu, May 28 2026

Crossrefs

Cf. A034836, A101423, A101424, A101425, A101427.

Sequence in context: A286733 A286773 A019541 * A296153 A190661 A233058

Adjacent sequences: A101423 A101424 A101425 * A101427 A101428 A101429

Keyword

nonn,changed

Author

Anthony C Robin, Jan 17 2005

Extensions

Edited and extended by Ray Chandler, Dec 19 2008

a(0)=7 prepended and g.f. edited by Alois P. Heinz, Oct 05 2016

Status

approved