|
%I #13 Sep 08 2022 08:44:42
%S 16,225,676,1369,2304,3481,4900,6561,8464,10609,12996,15625,18496,
%T 21609,24964,28561,32400,36481,40804,45369,50176,55225,60516,66049,
%U 71824,77841,84100,90601,97344,104329,111556,119025,126736,134689,142884,151321,160000,168921,178084,187489,197136
%N a(n) = (11*n + 4)^2.
%H G. C. Greubel, <a href="/A017438/b017438.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F From _Chai Wah Wu_, Jul 10 2016: (Start)
%F a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n > 2.
%F G.f.: (49*x^2 + 177*x + 16)/(1 - x)^3. (End)
%F E.g.f.: (16 + 209*x + 121*x^2)*exp(x). - _G. C. Greubel_, Sep 18 2019
%p seq((11*n+4)^2, n=0..50); # _G. C. Greubel_, Sep 18 2019
%t (11*Range[50] -7)^2 (* _G. C. Greubel_, Sep 18 2019 *)
%o (PARI) a(n)=(11*n+4)^2 \\ _Charles R Greathouse IV_, Jun 17 2017
%o (Magma) [(11*n+4)^2: n in [0..50]]; // _G. C. Greubel_, Sep 18 2019
%o (Sage) [(11*n+4)^2 for n in (0..50)] # _G. C. Greubel_, Sep 18 2019
%o (GAP) List([0..50], n-> (11*n+4)^2); # _G. C. Greubel_, Sep 18 2019
%Y Powers of the form (11*n+4)^m: A017437 (m=1), this sequence (m=2), A017439 (m=3), A017440 (m=4), A017441 (m=5), A017442 (m=6), A017443 (m=7), A017444 (m=8), A017445 (m=9), A017446 (m=10), A017447 (m=11), A017448 (m=12).
%K nonn,easy
%O 0,1
%A _N. J. A. Sloane_
%E Terms a(30) onward added by _G. C. Greubel_, Sep 18 2019
|
