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A016862 a(n) = (5*n + 1)^2.

%I A016862 #30 Feb 16 2025 08:32:33
%S A016862 1,36,121,256,441,676,961,1296,1681,2116,2601,3136,3721,4356,5041,
%T A016862 5776,6561,7396,8281,9216,10201,11236,12321,13456,14641,15876,17161,
%U A016862 18496,19881,21316,22801,24336,25921
%N A016862 a(n) = (5*n + 1)^2.
%H A016862 Ivan Panchenko, <a href="/A016862/b016862.txt">Table of n, a(n) for n = 0..200</a>
%H A016862 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/PolygammaFunction.html">Polygamma Function</a>.
%H A016862 Wikipedia, <a href="http://en.wikipedia.org/wiki/Polygamma_function">Polygamma Function</a>.
%H A016862 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F A016862 a(n) = 3*a(n-1) -3*a(n-2) +a(n-3). - _Harvey P. Dale_, Jul 11 2012
%F A016862 Sum_{n>=0} 1/a(n) = polygamma(1, 1/5)/25 = 1.050695088216... - _Amiram Eldar_, Oct 02 2020
%F A016862 G.f.: (1 +33*x +16*x^2)/(1-x)^3. - _Wesley Ivan Hurt_, Oct 02 2020
%F A016862 From _G. C. Greubel_, Dec 28 2022: (Start)
%F A016862 a(2*n) = A017282(n).
%F A016862 a(2*n+1) = 4*A016886(n).
%F A016862 E.g.f.: (1 + 35*x + 25*x^2)*exp(x). (End)
%t A016862 (5*Range[0,40]+1)^2 (* or *) LinearRecurrence[{3,-3,1},{1,36,121},40] (* _Harvey P. Dale_, Jul 11 2012 *)
%o A016862 (PARI) a(n)=(5*n+1)^2 \\ _Charles R Greathouse IV_, Jun 17 2017
%o A016862 (Magma) [(5*n+1)^2: n in [0..40]]; // _G. C. Greubel_, Dec 28 2022
%o A016862 (SageMath) [(5*n+1)^2 for n in range(41)] # _G. C. Greubel_, Dec 28 2022
%Y A016862 Sequences of the form (m*n+1)^2: A000012 (m=0), A000290 (m=1), A016754 (m=2), A016778 (m-3), A016814 (m=4), this sequence (m=5), A016922 (m=6), A016994 (m=7), A017078 (m=8), A017174 (m=9), A017282 (m=10), A017402 (m=11), A017534 (m=12), A134934 (m=14).
%K A016862 nonn,easy
%O A016862 0,2
%A A016862 _N. J. A. Sloane_