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A177073 a(n) = (9*n+4)*(9*n+5). 2
20, 182, 506, 992, 1640, 2450, 3422, 4556, 5852, 7310, 8930, 10712, 12656, 14762, 17030, 19460, 22052, 24806, 27722, 30800, 34040, 37442, 41006, 44732, 48620, 52670, 56882, 61256, 65792, 70490, 75350, 80372, 85556, 90902, 96410, 102080, 107912, 113906, 120062 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,1
COMMENTS
Cf. comment of Reinhard Zumkeller in A177059: in general, (h*n+h-k)*(h*n+k)=h^2*A002061(n+1)+(h-k)*k-h^2; therefore a(n)=81*A002061(n+1)-61. - Bruno Berselli, Aug 24 2010
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (3,-3,1).
FORMULA
a(n) = 162*n+a(n-1) with n>0, a(0)=20.
From Harvey P. Dale, Jun 24 2011: (Start)
a(0)=20, a(1)=182, a(2)=506, a(n) = 3*a(n-1)-3*a(n-2)+a(n-3).
G.f.: -2*(x*(10*x+61)+10)/(x-1)^3. (End)
From Amiram Eldar, Feb 19 2023: (Start)
a(n) = A017209(n)*A017221(n).
Sum_{n>=0} 1/a(n) = tan(Pi/18)*Pi/9.
Product_{n>=0} (1 - 1/a(n)) = sec(Pi/18)*cos(sqrt(5)*Pi/18).
Product_{n>=0} (1 + 1/a(n)) = sec(Pi/18)*cosh(sqrt(3)*Pi/18). (End)
MATHEMATICA
f[n_] := Module[{c = 9n}, (c+4)(c+5)]; Array[f, 40, 0] (* or *) LinearRecurrence[{3, -3, 1}, {20, 182, 506}, 40] (* Harvey P. Dale, Jun 24 2011 *)
PROG
(Magma) [(9*n+4)*(9*n+5): n in [0..50]]; // Vincenzo Librandi, Apr 08 2013
(PARI) a(n)=(9*n+4)*(9*n+5) \\ Charles R Greathouse IV, Jun 17 2017
CROSSREFS
Cf. A002061, A017209, A017221, A177059.
Sequence in context: A000144 A361609 A219581 * A211153 A210429 A367780
Adjacent sequences: A177070 A177071 A177072 * A177074 A177075 A177076
KEYWORD
nonn,easy
AUTHOR
Vincenzo Librandi, May 31 2010
EXTENSIONS
Edited by N. J. A. Sloane, Jun 22 2010
STATUS
approved

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Last modified July 18 18:59 EDT 2024. Contains 374388 sequences. (Running on oeis4.)