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A157660 a(n) = 8000*n - 40. 3
7960, 15960, 23960, 31960, 39960, 47960, 55960, 63960, 71960, 79960, 87960, 95960, 103960, 111960, 119960, 127960, 135960, 143960, 151960, 159960, 167960, 175960, 183960, 191960, 199960, 207960, 215960, 223960, 231960, 239960, 247960, 255960 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

The identity (80000*n^2 - 800*n + 1)^2 - (100*n^2 - n)*(8000*n - 40)^2 = 1 can be written as A157661(n)^2 - A157659(n)*a(n)^2 = 1 (see also the second part of the comment at A157661). - Vincenzo Librandi, Jan 28 2012

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 1..10000

Vincenzo Librandi, X^2-AY^2=1

Index entries for linear recurrences with constant coefficients, signature (2,-1).

FORMULA

a(n) = 2*a(n-1) - a(n-2). - Vincenzo Librandi, Jan 28 2012

G.f.: x*(40*x+7960)/(x-1)^2. - Vincenzo Librandi, Jan 28 2012

E.g.f.: 40*(1 - (1 - 200*x)*exp(x)). G. C. Greubel, Nov 17 2018

MATHEMATICA

LinearRecurrence[{2, -1}, {7960, 15960}, 40] (* Vincenzo Librandi, Jan 28 2012 *)

PROG

(Magma) I:=[7960, 15960]; [n le 2 select I[n] else 2*Self(n-1)-Self(n-2): n in [1..50]]; // Vincenzo Librandi, Jan 28 2012

(PARI) for(n=1, 40, print1(8000*n-40", ")); \\ Vincenzo Librandi, Jan 28 2012

(Sage) [40*(200*n - 1) for n in (1..40)] # G. C. Greubel, Nov 17 2018

(GAP) List([1..40], n -> 40*(200*n - 1)); # G. C. Greubel, Nov 17 2018

CROSSREFS

Cf. A157659, A157661.

Sequence in context: A293623 A316908 A254138 * A236786 A252190 A233730

Adjacent sequences: A157657 A157658 A157659 * A157661 A157662 A157663

KEYWORD

nonn,easy

AUTHOR

Vincenzo Librandi, Mar 04 2009

STATUS

approved

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Last modified December 3 11:54 EST 2022. Contains 358521 sequences. (Running on oeis4.)