cp's OEIS Frontend

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

%I A101424 #17 Oct 06 2016 07:31:58
%S A101424 4,9,18,28,42,57,76,96,120,145,174,204,238,273,312,352,396,441,490,
%T A101424 540,594,649,708,768,832,897,966,1036,1110,1185,1264,1344,1428,1513,
%U A101424 1602,1692,1786,1881,1980,2080,2184,2289,2398,2508,2622,2737,2856,2976,3100
%N A101424 Number of different cuboids with volume p^4 * q^n, where p,q are distinct prime numbers.
%C A101424 Subsequence of A034836, which gives the number of cuboids for volume n.
%F A101424 a(n) = A034836(2^4*3^n) = A034836(3^4*2^n) = A034836(p^4*q^n) for p,q distinct primes.
%F A101424 From _Colin Barker_, Mar 28 2014: (Start)
%F A101424 The following is conjectured.
%F A101424 a(n) = (29 + 3*(-1)^n + 36*n + 10*n^2)/8.
%F A101424 a(n) = 2*a(n-1) - 2*a(n-3) + a(n-4).
%F A101424 G.f.: -(x+4)/((x+1)*(x-1)^3). (End)
%Y A101424 Cf. A034836, A101423, A101425, A101426, A101427.
%K A101424 nonn
%O A101424 0,1
%A A101424 _Anthony C Robin_, Jan 17 2005
%E A101424 Edited and extended by _Ray Chandler_, Dec 19 2008
%E A101424 a(0)=4 prepended and g.f. edited by _Alois P. Heinz_, Oct 05 2016