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%I #28 Sep 08 2022 08:45:41
%S 2026,8102,18228,32404,50630,72906,99232,129608,164034,202510,245036,
%T 291612,342238,396914,455640,518416,585242,656118,731044,810020,
%U 893046,980122,1071248,1166424,1265650,1368926,1476252,1587628,1703054,1822530
%N a(n) = 2025*n^2 + n.
%C The identity (32805000*n^2 + 16200*n + 1)^2 - (2025*n^2 + n)*(729000*n + 180)^2 = 1 can be written as A157081(n)^2 - a(n)*A156868(n)^2 = 1.
%H Vincenzo Librandi, <a href="/A156856/b156856.txt">Table of n, a(n) for n = 1..10000</a>
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F From _R. J. Mathar_, Mar 09 2009: (Start)
%F a(n) = 3*a(n-1) -3*a(n-2) +a(n-3).
%F G.f.: 2*x*(1013 + 1012*x)/(1-x)^3. (End)
%F E.g.f.: x*(2026 + 2025*x)*exp(x). - _G. C. Greubel_, Jan 28 2022
%t LinearRecurrence[{3,-3,1},{2026,8102,18228},40]
%o (Magma) I:=[2026, 8102, 18228]; [n le 3 select I[n] else 3*Self(n-1)-3*Self(n-2)+1*Self(n-3): n in [1..40]];
%o (PARI) a(n)=n*(2025*n+1) \\ _Charles R Greathouse IV_, Dec 23 2011
%o (Sage) [n*(2025*n +1) for n in (1..40)] # _G. C. Greubel_, Jan 28 2022
%Y Cf. A156855, A156868, A157081.
%Y A subsequence of A031768.
%K nonn,easy
%O 1,1
%A _Vincenzo Librandi_, Feb 17 2009
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