The On-Line Encyclopedia of Integer Sequences (OEIS)

A157736 revision #13

A157736

388962n^2 - 347508n + 77617.

119071, 938449, 2535751, 4910977, 8064127, 11995201, 16704199, 22191121, 28455967, 35498737, 43319431, 51918049, 61294591, 71449057, 82381447, 94091761, 106579999, 119846161, 133890247, 148712257, 164312191, 180690049

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OFFSET

1,1

COMMENTS

The identity (388962*n^2-347508*n+77617)^2-(441*n^2-394*n+88)*(18522*n- 8274)^2=1 can be written as a(n)^2-A157734(n)*A157735(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*(-119071-581236*x-77617*x^2)/(x-1)^3.

MATHEMATICA

LinearRecurrence[{3, -3, 1}, {119071, 938449, 2535751}, 40]

PROG

(MAGMA) I:=[119071, 938449, 2535751]; [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) = 388962*n^2 - 347508*n + 77617.

CROSSREFS

Cf. A157734, A157735.

Sequence in context: A253867 A253874 A253540 * A031686 A262510 A262509

Adjacent sequences: A157733 A157734 A157735 * A157737 A157738 A157739

KEYWORD

nonn,easy

AUTHOR

Vincenzo Librandi, Mar 05 2009

STATUS

approved