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%I A028569 #64 Feb 12 2024 02:28:28
%S A028569 0,10,22,36,52,70,90,112,136,162,190,220,252,286,322,360,400,442,486,
%T A028569 532,580,630,682,736,792,850,910,972,1036,1102,1170,1240,1312,1386,
%U A028569 1462,1540,1620,1702,1786,1872,1960,2050,2142,2236,2332,2430
%N A028569 a(n) = n*(n + 9).
%C A028569 a(n) is the first Zagreb index of the wheel graph with n + 1 vertices. The first Zagreb index of a simple connected graph is the sum of the squared degrees of its vertices. Alternately, it is the sum of the degree sums d(i) + d(j) over all edges ij of the graph. - _Emeric Deutsch_, Nov 07 2016
%C A028569 The sequence provides all nonnegative k such that 4*k + 81 is a square. - _Bruno Berselli_, May 08 2018
%H A028569 Shawn A. Broyles, <a href="/A028569/b028569.txt">Table of n, a(n) for n = 0..1000</a>
%H A028569 Patrick De Geest, <a href="http://www.worldofnumbers.com/consemor.htm">Palindromic Quasipronics of the form n(n+x)</a>.
%H A028569 Felix Pozon 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 A028569 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F A028569 Equals 2 * A056000. - _Zerinvary Lajos_, Feb 12 2007
%F A028569 a(n) = 2*n + a(n - 1) + 8. - _Vincenzo Librandi_, Aug 05 2010
%F A028569 Sum_{n >= 1} 1/a(n) = 7129/22680 = 0.314329806... - _R. J. Mathar_, Mar 22 2011
%F A028569 G.f.: 2*x*(5 - 4*x)/(1 - x)^3. - _Colin Barker_, Jan 10 2012
%F A028569 a(n) = 3*a(n - 1) - 3*a(n - 2) + a(n - 3). - _Wesley Ivan Hurt_, Sep 26 2014
%F A028569 Sum_{n>=1} (-1)^(n+1)/a(n) = 2*log(2)/9 - 1879/22680. - _Amiram Eldar_, Jan 15 2021
%F A028569 From _Amiram Eldar_, Feb 12 2024: (Start)
%F A028569 Product_{n>=1} (1 - 1/a(n)) = -128*cos(sqrt(85)*Pi/2)/(19*Pi).
%F A028569 Product_{n>=1} (1 + 1/a(n)) = 51840*cos(sqrt(77)*Pi/2)/(4199*Pi). (End)
%p A028569 A028569:=n->n*(n+9): seq(A028569(n), n=0..50); # _Wesley Ivan Hurt_, Sep 26 2014
%t A028569 Table[n (n + 9), {n, 0, 50}] (* _Wesley Ivan Hurt_, Sep 26 2014 *)
%o A028569 (Magma) [n*(n+9) : n in [0..50]]; // _Wesley Ivan Hurt_, Sep 26 2014
%o A028569 (PARI) a(n)=n*(n+9) \\ _Charles R Greathouse IV_, Sep 24 2015
%o A028569 (Scala) (0 to 49).map(n => n * (n + 9)) // _Alonso del Arte_, Apr 22 2020
%Y A028569 Cf. A056000.
%K A028569 nonn,easy
%O A028569 0,2
%A A028569 _Patrick De Geest_

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