%I #41 Dec 25 2022 03:52:42

%S 1,121,441,961,1681,2601,3721,5041,6561,8281,10201,12321,14641,17161,

%T 19881,22801,25921,29241,32761,36481,40401,44521,48841,53361,58081,

%U 63001,68121,73441,78961,84681,90601,96721,103041,109561,116281,123201

%N a(n) = (10*n + 1)^2.

%H Vincenzo Librandi, <a href="/A017282/b017282.txt">Table of n, a(n) for n = 0..10000</a>

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).

%F G.f.: (1+118*x+81*x^2)/(1-x)^3. - _Bruno Berselli_, Jul 30 2011

%F a(n) = a(n-1) + 40*(5*n-2), n > 0; a(0)=1. - _Miquel Cerda_, Oct 30 2016

%F a(n) = A017281(n)^2. - _Michel Marcus_, Oct 30 2016

%F E.g.f.: (1 +120*x +100*x^2)*exp(x). - _G. C. Greubel_, Dec 24 2022

%t (* Programs from _Michael De Vlieger_, Mar 30 2017 *)

%t Table[(10 n+1)^2, {n, 0, 35}]

%t FoldList[#1 + 200 #2 - 80 &, 1, Range@ 35]

%t CoefficientList[Series[(1+118x+81x^2)/(1-x)^3, {x,0,35}], x] (* End *)

%t LinearRecurrence[{3,-3,1},{1,121,441},40] (* _Harvey P. Dale_, Sep 21 2017 *)

%o (Magma) [(10*n+1)^2: n in [0..35]]; // _Vincenzo Librandi_, Jul 30 2011

%o (PARI) for(n=0, 35, print1((10*n+1)^2", ")); \\ _Bruno Berselli_, Jul 30 2011

%o (SageMath) [(10*n+1)^2 for n in range(51)] # _G. C. Greubel_, Dec 24 2022

%Y Sequences of the form (m*n+1)^2: A000012 (m=0), A000290 (m=1), A016754 (m=2), A016778 (m=3), A016814 (m=4), A016862 (m=5), A016922 (m=6), A016994 (m=7), A017078 (m=8), A017174 (m=9), this sequence (m=10), A017402 (m=11), A017534 (m=12), A134934 (m=14).

%Y Cf. A017281.

%K nonn,easy

%O 0,2

%A _N. J. A. Sloane_

%E More terms from _Bruno Berselli_, Jul 30 2011