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A157651 a(n) = 100*n^2 - 49*n + 6. 3
57, 308, 759, 1410, 2261, 3312, 4563, 6014, 7665, 9516, 11567, 13818, 16269, 18920, 21771, 24822, 28073, 31524, 35175, 39026, 43077, 47328, 51779, 56430, 61281, 66332, 71583, 77034, 82685, 88536, 94587, 100838, 107289, 113940, 120791, 127842 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

The identity (80000*n^2 -39200*n +4801)^2 - (100*n^2 -49*n +6)*(8000*n -1960)^2 = 1 can be written as A157653(n)^2 - a(n)*A157652(n)^2 = 1.

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 (3,-3,1).

FORMULA

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

G.f.: x*(57 + 137*x + 6*x^2)/(1-x)^3.

E.g.f.: (6 + 51*x + 100*x^2)*exp(x) - 6. - G. C. Greubel, Nov 17 2018

MATHEMATICA

LinearRecurrence[{3, -3, 1}, {57, 308, 759}, 40]

PROG

(MAGMA) I:=[57, 308, 759]; [n le 3 select I[n] else 3*Self(n-1)-3*Self(n-2)+1*Self(n-3): n in [1..40]];

(PARI) a(n) = 100*n^2 - 49*n + 6.

(Sage) [100*n^2-49*n+6 for n in (1..40)] # G. C. Greubel, Nov 17 2018

(GAP) List([1..40], n -> 100*n^2-49*n+6); # G. C. Greubel, Nov 17 2018

CROSSREFS

Cf. A157652, A157653.

Sequence in context: A145296 A176635 A048422 * A251263 A043399 A038482

Adjacent sequences:  A157648 A157649 A157650 * A157652 A157653 A157654

KEYWORD

nonn,easy

AUTHOR

Vincenzo Librandi, Mar 03 2009

STATUS

approved

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Last modified August 7 12:01 EDT 2022. Contains 355985 sequences. (Running on oeis4.)