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A028569
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a(n) = n*(n + 9).
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21
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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
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OFFSET
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0,2
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COMMENTS
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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
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LINKS
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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, March 2014; Preprint on ResearchGate.
Index entries for linear recurrences with constant coefficients, signature (3,-3,1).
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FORMULA
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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
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MAPLE
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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
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MATHEMATICA
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Table[n (n + 9), {n, 0, 50}] (* Wesley Ivan Hurt, Sep 26 2014 *)
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PROG
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(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
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CROSSREFS
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Cf. A056000.
Sequence in context: A276626 A211482 A177791 * A014367 A063710 A157917
Adjacent sequences: A028566 A028567 A028568 * A028570 A028571 A028572
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KEYWORD
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nonn,easy
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AUTHOR
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Patrick De Geest
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STATUS
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approved
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