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a(n) = (8*n + 1)^6.
1

%I #15 Sep 08 2022 08:44:41

%S 1,531441,24137569,244140625,1291467969,4750104241,13841287201,

%T 34296447249,75418890625,151334226289,282429536481,496981290961,

%U 832972004929,1340095640625,2081951752609,3138428376721

%N a(n) = (8*n + 1)^6.

%H Vincenzo Librandi, <a href="/A017082/b017082.txt">Table of n, a(n) for n = 0..10000</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) = 7*a(n-1) - 21*a(n-2) + 35*a(n-3) - 35*a(n-4) + 21*a(n-5) - 7*a(n-6) + a(n-7); a(0)=1, a(1)=531441, a(2)=24137569, a(3)=244140625, a(4)=1291467969, a(5)=4750104241, a(6)=13841287201. - _Harvey P. Dale_, Dec 18 2012

%t (8*Range[0,30]+1)^6 (* or *) LinearRecurrence[{7,-21,35,-35,21,-7,1},{1,531441,24137569,244140625,1291467969,4750104241,13841287201},30] (* _Harvey P. Dale_, Dec 18 2012 *)

%o (Magma) [(8*n+1)^6: n in [0..30]]; // _Vincenzo Librandi_, Jul 11 2011

%K nonn,easy

%O 0,2

%A _N. J. A. Sloane_