A158536 - OEIS

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A158536

a(n) = 121*n^2 + 11.

2

11, 132, 495, 1100, 1947, 3036, 4367, 5940, 7755, 9812, 12111, 14652, 17435, 20460, 23727, 27236, 30987, 34980, 39215, 43692, 48411, 53372, 58575, 64020, 69707, 75636, 81807, 88220, 94875, 101772, 108911, 116292, 123915, 131780, 139887, 148236, 156827, 165660

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OFFSET

0,1

COMMENTS

The identity (22*n^2+1)^2-(121*n^2+11) * (2*n)^2 = 1 can be written as A158537(n)^2 -a(n) * A005843(n)^2 = 1.

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..10000

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

FORMULA

From R. J. Mathar, Oct 16 2009: (Start)

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

G.f.: 11*(1+9*x+12*x^2)/(1-x)^3. (End)

From Amiram Eldar, Mar 06 2023: (Start)

Sum_{n>=0} 1/a(n) = (coth(Pi/sqrt(11))*Pi/sqrt(11) + 1)/22.

Sum_{n>=0} (-1)^n/a(n) = (cosech(Pi/sqrt(11))*Pi/sqrt(11) + 1)/22. (End)

MATHEMATICA

121Range[0, 40]^2+11 (* Harvey P. Dale, Mar 04 2011 *)

LinearRecurrence[{3, -3, 1}, {11, 132, 495}, 50] (* Vincenzo Librandi, Feb 12 2012 *)

PROG

(Magma) I:=[11, 132, 495]; [n le 3 select I[n] else 3*Self(n-1)-3*Self(n-2)+1*Self(n-3): n in [1..40]]; // Vincenzo Librandi, Feb 12 2012

(PARI) for(n=1, 40, print1(121*n^2+11", ")); \\ Vincenzo Librandi, Feb 12 2012

CROSSREFS

Cf. A005843, A158537.

Sequence in context: A068645 A097258 A044041 * A229252 A242163 A105280

Adjacent sequences: A158533 A158534 A158535 * A158537 A158538 A158539

KEYWORD

nonn,less,easy

AUTHOR

Vincenzo Librandi, Mar 21 2009

EXTENSIONS

a(0) added by R. J. Mathar, Oct 16 2009

STATUS

approved