OFFSET
0,2
COMMENTS
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
The sequence provides all nonnegative k such that 4*k + 81 is a square. - Bruno Berselli, May 08 2018
LINKS
Shawn A. Broyles, Table of n, a(n) for n = 0..1000
Patrick De Geest, Palindromic Quasipronics of the form n(n+x).
Felix Pozon Muga II, Extending the Golden Ratio and the Binet-de Moivre Formula, Preprint on ResearchGate, March 2014.
Index entries for linear recurrences with constant coefficients, signature (3,-3,1).
FORMULA
a(n) = 2*A056000(n). - Zerinvary Lajos, Feb 12 2007
a(n) = 2*n + a(n - 1) + 8. - Vincenzo Librandi, Aug 05 2010
Sum_{n >= 1} 1/a(n) = 7129/22680 = 0.314329806... - R. J. Mathar, Mar 22 2011
G.f.: 2*x*(5 - 4*x)/(1 - x)^3. - Colin Barker, Jan 10 2012
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3). - Wesley Ivan Hurt, Sep 26 2014
Sum_{n>=1} (-1)^(n+1)/a(n) = 2*log(2)/9 - 1879/22680. - Amiram Eldar, Jan 15 2021
From Amiram Eldar, Feb 12 2024: (Start)
Product_{n>=1} (1 - 1/a(n)) = -128*cos(sqrt(85)*Pi/2)/(19*Pi).
Product_{n>=1} (1 + 1/a(n)) = 51840*cos(sqrt(77)*Pi/2)/(4199*Pi). (End)
E.g.f.: exp(x)*x*(10 + x). - Elmo R. Oliveira, Dec 12 2024
MAPLE
MATHEMATICA
Table[n (n + 9), {n, 0, 50}] (* Wesley Ivan Hurt, Sep 26 2014 *)
PROG
(Magma) [n*(n+9) : n in [0..50]]; // Wesley Ivan Hurt, Sep 26 2014
(PARI) a(n)=n*(n+9) \\ Charles R Greathouse IV, Sep 24 2015
(Scala) (0 to 49).map(n => n * (n + 9)) // Alonso del Arte, Apr 22 2020
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
STATUS
approved