cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A017378 a(n) = (10*n + 9)^2.

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%I A017378 #30 Sep 08 2022 08:44:42
%S A017378 81,361,841,1521,2401,3481,4761,6241,7921,9801,11881,14161,16641,
%T A017378 19321,22201,25281,28561,32041,35721,39601,43681,47961,52441,57121,
%U A017378 62001,67081,72361,77841,83521,89401,95481,101761,108241,114921,121801,128881,136161,143641
%N A017378 a(n) = (10*n + 9)^2.
%H A017378 Vincenzo Librandi, <a href="/A017378/b017378.txt">Table of n, a(n) for n = 0..10000</a>
%H A017378 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F A017378 From _Colin Barker_, Mar 30 2017: (Start)
%F A017378 G.f.: (81 + 118*x + x^2) / (1 - x)^3.
%F A017378 a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>2.
%F A017378 (End)
%p A017378 A017378:=n->(10*n+9)^2: seq(A017378(n), n=0..50); # _Wesley Ivan Hurt_, Mar 30 2017
%t A017378 Table[(10 n + 9)^2, {n, 0, 37}] (* or *)
%t A017378 LinearRecurrence[{3, -3, 1}, {81, 361, 841}, 38] (* or *)
%t A017378 CoefficientList[Series[(81 + 118 x + x^2)/(1 - x)^3, {x, 0, 37}], x] (* _Michael De Vlieger_, Mar 30 2017 *)
%o A017378 (Magma) [(10*n+9)^2: n in [0..40]]; // _Vincenzo Librandi_, Aug 31 2011
%o A017378 (PARI) a(n) = (10*n+9)^2; \\ _Michel Marcus_, Aug 26 2015
%o A017378 (PARI) Vec((81 + 118*x + x^2) / (1 - x)^3 + O(x^40)) \\ _Colin Barker_, Mar 30 2017
%Y A017378 Cf. A017377.
%K A017378 nonn,easy
%O A017378 0,1
%A A017378 _N. J. A. Sloane_