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%I #49 Mar 14 2022 02:45:12
%S 0,22,46,72,100,130,162,196,232,270,310,352,396,442,490,540,592,646,
%T 702,760,820,882,946,1012,1080,1150,1222,1296,1372,1450,1530,1612,
%U 1696,1782,1870,1960,2052,2146,2242,2340,2440,2542,2646,2752,2860,2970,3082,3196,3312
%N a(n) = n*(n+21).
%H G. C. Greubel, <a href="/A132763/b132763.txt">Table of n, a(n) for n = 0..5000</a>
%H Felix P. Muga II, <a href="https://www.researchgate.net/publication/267327689_Extending_the_Golden_Ratio_and_the_Binet-de_Moivre_Formula">Extending the Golden Ratio and the Binet-de Moivre Formula</a>, Preprint on ResearchGate, March 2014.
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F a(n) = n*(n + 21).
%F a(n) = 2*n + a(n-1) + 20 (with a(0)=0). - _Vincenzo Librandi_, Aug 03 2010
%F a(0)=0, a(1)=22, a(2)=46, a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3). - _Harvey P. Dale_, May 25 2014
%F From _Amiram Eldar_, Jan 16 2021: (Start)
%F Sum_{n>=1} 1/a(n) = H(21)/21 = A001008(21)/A102928(21) = 18858053/108636528, where H(k) is the k-th harmonic number.
%F Sum_{n>=1} (-1)^(n+1)/a(n) = 2*log(2)/21 - 166770367/4888643760. (End)
%F From _Stefano Spezia_, Jan 30 2021: (Start)
%F O.g.f.: 2*x*(11 - 10*x)/(1 - x)^3.
%F E.g.f.: x*(22 + x)*exp(x). (End)
%t Table[n(n+21),{n,0,50}] (* or *) LinearRecurrence[{3,-3,1},{0,22,46},50] (* _Harvey P. Dale_, May 25 2014 *)
%o (PARI) a(n)=n*(n+21) \\ _Charles R Greathouse IV_, Oct 07 2015
%o (Sage) [n*(n+21) for n in (0..50)] # _G. C. Greubel_, Mar 14 2022
%Y Cf. A001008, A002378, A005563, A028347, A028552, A028557, A028560, A028563, A028566, A028569, A098603, A098847, A098848, A098849, A098850, A102928, A120071, A132759, A132760, A132761, A132762, A132764, A132765, A132766, A132767.
%K easy,nonn
%O 0,2
%A _Omar E. Pol_, Aug 28 2007
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