A132766 - OEIS

%I #28 Mar 14 2022 02:45:09

%S 0,25,52,81,112,145,180,217,256,297,340,385,432,481,532,585,640,697,

%T 756,817,880,945,1012,1081,1152,1225,1300,1377,1456,1537,1620,1705,

%U 1792,1881,1972,2065,2160,2257,2356,2457,2560,2665,2772,2881,2992,3105,3220,3337

%N a(n) = n*(n+24).

%H G. C. Greubel, <a href="/A132766/b132766.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 + 24).

%F a(n) = 2*n + a(n-1) + 23 (with a(0)=0). - _Vincenzo Librandi_, Aug 03 2010

%F a(0)=0, a(1)=25, a(2)=52; for n>2, a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3). - _Harvey P. Dale_, Feb 11 2016

%F From _Amiram Eldar_, Jan 16 2021: (Start)

%F Sum_{n>=1} 1/a(n) = H(24)/24 = A001008(24)/A102928(24) = 1347822955/8566766208, where H(k) is the k-th harmonic number.

%F Sum_{n>=1} (-1)^(n+1)/a(n) = 3602044091/128501493120. (End)

%F From _G. C. Greubel_, Mar 14 2022: (Start)

%F G.f.: 2*x*(13 - 12*x)/(1-x)^3.

%F E.g.f.: x*(26 + x)*exp(x). (End)

%t Table[n (n + 24), {n, 0, 50}] (* or *) LinearRecurrence[{3, -3, 1}, {0, 25, 52}, 50] (* _Harvey P. Dale_, Feb 11 2016 *)

%o (PARI) a(n)=n*(n+24) \\ _Charles R Greathouse IV_, Jun 17 2017

%o (Sage) [n*(n+24) for n in (0..50)] # _G. C. Greubel_, Mar 14 2022

%Y Cf. A001008, A002378, A005563, A028347, A028552, A028557, A028560, A028563, A028566, A028569, A098603, A098849, A098850, A098847, A098848, A102928, A120071, A132759, A132760, A132761, A132762, A132763, A132764, A132765.

%K easy,nonn

%O 0,2

%A _Omar E. Pol_, Aug 28 2007