A017466 - OEIS

%I #20 Sep 08 2022 08:44:42

%S 46656,24137569,481890304,3518743761,15625000000,51520374361,

%T 139314069504,326940373369,689869781056,1340095640625,2436396322816,

%U 4195872914689,6906762437184,10942526586601,16777216000000,25002110044521,36343632130624,51682540549249,72074394832896

%N a(n) = (11*n + 6)^6.

%H Vincenzo Librandi, <a href="/A017466/b017466.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(0) = 46656, a(1) = 24137569, a(2) = 481890304, a(3) = 3518743761, a(4) = 15625000000, a(5) = 51520374361, a(6) = 139314069504, 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). - _Harvey P. Dale_, Jan 19 2013

%F From _G. C. Greubel_, Sep 19 2019: (Start)

%F G.f.: (46656 +23810977*x +313907097*x^2 +650767622*x^3 +270308102*x^4 +16667841*x^5 +15625*x^6)/(1-x)^7.

%F E.g.f.: (46656 +24090913*x +216830911*x^2 +357573150*x^3 +181035965*x^4 +32371251*x^5 +1771561*x^6)*exp(x). (End)

%p seq((11*n+6)^6, n=0..20); # _G. C. Greubel_, Sep 19 2019

%t (11 * Range[0, 20] + 6)^6 (* or *) LinearRecurrence[{7, -21, 35, -35, 21, -7, 1}, {46656, 24137569, 481890304, 3518743761, 15625000000, 51520374361, 139314069504}, 20] (* _Harvey P. Dale_, Jan 19 2013 *)

%o (Magma) [(11*n+6)^6: n in [0..20]]; // _Vincenzo Librandi_, Sep 04 2011

%o (PARI) a(n)=(11*n+6)^6 \\ _Charles R Greathouse IV_, Nov 04 2017

%o (Sage) [(11*n+6)^6 for n in (0..20)] # _G. C. Greubel_, Sep 19 2019

%o (GAP) List([0..20], n-> (11*n+6)^6); # _G. C. Greubel_, Sep 19 2019

%Y Powers of the form (11*n+6)^m: A017461 (m=1), A017462 (m=2), A017463 (m=3), A017464 (m=4), A017465 (m=5), this sequence (m=6), A017467 (m=7), A017468 (m=8), A017469 (m=9), A017470 (m=10), A017471 (m=11), A017472 (m=12).

%K nonn,easy

%O 0,1

%A _N. J. A. Sloane_