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A028569 a(n) = n*(n + 9). 20
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 (list; graph; refs; listen; history; text; internal format)
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

REFERENCES

F. P. Muga II, Extending the Golden Ratio and the Binet-de Moivre Formula, March 2014; Preprint on ResearchGate.

LINKS

Table of n, a(n) for n=0..45.

P. De Geest, Palindromic Quasipronics of the form n(n+x)

Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

FORMULA

Equals 2*A056000. - 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

MAPLE

with(finance):seq(add(cashflows([2, k, k], 0 ), k=4..n), n=3..51); # Zerinvary Lajos, Jun 30 2008

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 *)

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

CROSSREFS

Cf. A056000.

Sequence in context: A276626 A211482 A177791 * A014367 A063710 A157917

Adjacent sequences:  A028566 A028567 A028568 * A028570 A028571 A028572

KEYWORD

nonn,easy

AUTHOR

Patrick De Geest

STATUS

approved

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Last modified December 9 12:25 EST 2016. Contains 278971 sequences.