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%I #18 Dec 29 2022 06:32:19
%S 1,81,289,625,1089,1681,2401,3249,4225,5329,6561,7921,9409,11025,
%T 12769,14641,16641,18769,21025,23409,25921,28561,31329,34225,37249,
%U 40401,43681,47089,50625,54289,58081
%N a(n) = (8*n + 1)^2.
%H Vincenzo Librandi, <a href="/A017078/b017078.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 + 78*x + 49*x^2)/(1-x)^3. - _R. J. Mathar_, Mar 21 2016
%F From _G. C. Greubel_, Dec 28 2022: (Start)
%F a(2*n) = A016754(8*n).
%F E.g.f.: (1 + 80*x + 64*x^2)*exp(x). (End)
%t (8*Range[0,40] +1)^2 (* _G. C. Greubel_, Dec 28 2022 *)
%o (Magma) [(8*n+1)^2: n in [0..40]]; // _Vincenzo Librandi_, Jul 11 2011
%o (PARI) a(n)=(8*n+1)^2 \\ _Charles R Greathouse IV_, Jun 17 2017
%o (SageMath) [(8*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), this sequence (m=8), A017174 (m=9), A017282 (m=10), A017402 (m=11), A017534 (m=12), A134934 (m=14).
%K nonn,easy
%O 0,2
%A _N. J. A. Sloane_
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