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A158643 a(n) = 676*n^2 + 26. 2
26, 702, 2730, 6110, 10842, 16926, 24362, 33150, 43290, 54782, 67626, 81822, 97370, 114270, 132522, 152126, 173082, 195390, 219050, 244062, 270426, 298142, 327210, 357630, 389402, 422526, 457002, 492830, 530010, 568542, 608426, 649662, 692250 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

The identity (52*n^2 + 1)^2 - (676*n^2 + 26)*(2*n)^2 = 1 can be written as A158644(n)^2 - a(n)*A005843(n)^2 = 1.

LINKS

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

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

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

FORMULA

G.f.: -26*(1 + 24*x + 27*x^2)/(x-1)^3.

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

MATHEMATICA

26(26Range[0, 40]^2+1) (* Harvey P. Dale, Mar 30 2011 *)

LinearRecurrence[{3, -3, 1}, {26, 702, 2730}, 50] (* Vincenzo Librandi, Feb 17 2012 *)

PROG

(MAGMA) I:=[26, 702, 2730]; [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 17 2012

(PARI) for(n=0, 40, print1(676*n^2 + 26", ")); \\ Vincenzo Librandi, Feb 17 2012

CROSSREFS

Cf. A005843, A158644.

Sequence in context: A041313 A042302 A097835 * A181227 A094738 A182612

Adjacent sequences:  A158640 A158641 A158642 * A158644 A158645 A158646

KEYWORD

nonn,easy

AUTHOR

Vincenzo Librandi, Mar 23 2009

EXTENSIONS

Comment rephrased and redundant formula replaced by R. J. Mathar, Oct 19 2009

STATUS

approved

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Last modified April 5 13:02 EDT 2020. Contains 333241 sequences. (Running on oeis4.)