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a(n) = 648 * n^6.
1

%I #30 Jun 25 2017 23:04:09

%S 0,648,41472,472392,2654208,10125000,30233088,76236552,169869312,

%T 344373768,648000000,1147971528,1934917632,3127772232,4879139328,

%U 7381125000,10871635968,15641144712,22039921152,30485730888,41472000000,55576446408,73470177792,95927256072

%N a(n) = 648 * n^6.

%C Numbers n such that n/2 is a square and n/3 is a cube.

%H G. C. Greubel, <a href="/A185270/b185270.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (7,-21,35,-35,21,-7,1).

%F a(n) = 648*n^6 = 648*A001014(n).

%F G.f.: -648*x*(x+1)*(x^4+56*x^3+246*x^2+56*x+1) / (x-1)^7.

%e 41472 is a member since 41472/2 = 20736 = 144^2 and 41472/3 = 13824 = 24^3.

%t Table[648*n^6, {n, 0, 23}] (* _Zak Seidov_, Jun 11 2015 *)

%t LinearRecurrence[{7,-21,35,-35,21,-7,1},{0,648,41472,472392,2654208,10125000,30233088},30] (* _Harvey P. Dale_, Mar 31 2016 *)

%o (PARI) a(n)=648*n^6 \\ _Charles R Greathouse IV_, Jun 11 2015

%Y Cf. A000290, A000578, A001014.

%K nonn,easy

%O 0,2

%A _Jayanta Basu_, Apr 23 2013