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A098850 a(n) = n*(n + 18). 18
0, 19, 40, 63, 88, 115, 144, 175, 208, 243, 280, 319, 360, 403, 448, 495, 544, 595, 648, 703, 760, 819, 880, 943, 1008, 1075, 1144, 1215, 1288, 1363, 1440, 1519, 1600, 1683, 1768, 1855, 1944, 2035, 2128, 2223, 2320, 2419, 2520, 2623, 2728, 2835, 2944, 3055 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

REFERENCES

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

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..1000

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

FORMULA

a(n) = (n+9)^2 - 9^2 = n*(n + 18), n>=0.

G.f.: x*(19 - 17*x)/(1-x)^3.

a(n) = 2*n + a(n-1) + 17 (with a(0)=0). - Vincenzo Librandi, Nov 17 2010

From G. C. Greubel, Jul 29 2016: (Start)

a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3).

E.g.f.: x*(19 + x)*exp(x). (End)

MAPLE

seq(n*(n+18), n=0..52); # (Deutsch)

MATHEMATICA

s=0; lst={}; Do[s+=n; AppendTo[lst, s], {n, 19, 6!, 2}]; lst (* Vladimir Joseph Stephan Orlovsky, Feb 26 2009 *)

LinearRecurrence[{3, -3, 1}, {0, 19, 40}, 25] (* G. C. Greubel, Jul 29 2016 *)

CROSSREFS

Cf. A098832.

a(n-9), n>=10, ninth column (used for the n=9 series of the hydrogen atom) of triangle A120070.

Sequence in context: A041716 A041718 A041720 * A264537 A164078 A128677

Adjacent sequences:  A098847 A098848 A098849 * A098851 A098852 A098853

KEYWORD

nonn,easy

AUTHOR

Eugene McDonnell (eemcd(AT)mac.com), Nov 04 2004

EXTENSIONS

More terms from Emeric Deutsch, Mar 06 2005

STATUS

approved

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Last modified December 9 21:41 EST 2016. Contains 278987 sequences.