A028569 a(n) = n*(n + 9).

0, 10, 22, 36, 52, 70, 90, 112, 136, 162, 190, 220, 252, 286, 322, 360, 400, 442, 486, 532, 580, 630, 682, 736, 792, 850, 910, 972, 1036, 1102, 1170, 1240, 1312, 1386, 1462, 1540, 1620, 1702, 1786, 1872, 1960, 2050, 2142, 2236, 2332, 2430, 2530, 2632, 2736, 2842

Offset: 0

Author

Patrick De Geest

Keywords

• nonn
• easy

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).

Crossrefs

Cf. A056000.

Programs

Magma

[n*(n+9) : n in [0..50]]; // Wesley Ivan Hurt, Sep 26 2014

Maple

A028569:=n->n*(n+9): seq(A028569(n), n=0..50); # Wesley Ivan Hurt, Sep 26 2014

Mathematica

Table[n (n + 9), {n, 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

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