A101425 - OEIS

%I #16 Oct 06 2016 07:32:10

%S 5,12,24,38,57,78,104,132,165,200,240,282,329,378,432,488,549,612,680,

%T 750,825,902,984,1068,1157,1248,1344,1442,1545,1650,1760,1872,1989,

%U 2108,2232,2358,2489,2622,2760,2900,3045,3192,3344,3498,3657,3818,3984,4152

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

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

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

%F From _Colin Barker_, Mar 28 2014: (Start)

%F The following is conjectured.

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

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

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

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

%K nonn

%O 0,1

%A _Anthony C Robin_, Jan 17 2005

%E Edited and extended by _Ray Chandler_, Dec 19 2008

%E a(0)=5 prepended and g.f. edited by _Alois P. Heinz_, Oct 05 2016