A017174 - OEIS

%I #24 Feb 25 2024 11:20:03

%S 1,100,361,784,1369,2116,3025,4096,5329,6724,8281,10000,11881,13924,

%T 16129,18496,21025,23716,26569,29584,32761,36100,39601,43264,47089,

%U 51076,55225,59536,64009,68644

%N a(n) = (9*n + 1)^2.

%H Vincenzo Librandi, <a href="/A017174/b017174.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.: x*(1 + 97*x + 64*x^2)/(1-x)^3. - _Bruno Berselli_, Aug 25 2011

%F From _G. C. Greubel_, Dec 28 2022: (Start)

%F a(2*n) = A016754(9*n).

%F a(2*n+1) = 4*A017222(n).

%F E.g.f.: (1 + 99*x + 81*x^2)*exp(x). (End)

%t (9*Range[0,40] +1)^2 (* _G. C. Greubel_, Dec 28 2022 *)

%t LinearRecurrence[{3,-3,1},{1,100,361},50] (* _Harvey P. Dale_, Feb 25 2024 *)

%o (Magma) [(9*n+1)^2: n in [0..40]]; // _Vincenzo Librandi_, Aug 25 2011

%o (PARI) a(n)=(9*n+1)^2 \\ _Charles R Greathouse IV_, Jun 17 2017

%o (SageMath) [(9*n+1)^2 for n in range(41)] # _G. C. Greubel_, Dec 28 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), this sequence (m=9), A017282 (m=10), A017402 (m=11), A017534 (m=12), A134934 (m=14).

%Y Cf. A017222.

%K nonn,easy

%O 0,2

%A _N. J. A. Sloane_