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A158484 49n^2 - 7. 2
42, 189, 434, 777, 1218, 1757, 2394, 3129, 3962, 4893, 5922, 7049, 8274, 9597, 11018, 12537, 14154, 15869, 17682, 19593, 21602, 23709, 25914, 28217, 30618, 33117, 35714, 38409, 41202, 44093, 47082, 50169, 53354, 56637, 60018, 63497, 67074 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

The identity (14*n^2-1)^2-(49*n^2-7)*(2*n)^2=1 can be written as A158485(n)^2-a(n)*A005843(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: 7*x*(-6-9*x+x^2)/(x-1)^3.

MATHEMATICA

LinearRecurrence[{3, -3, 1}, {42, 189, 434}, 50]

PROG

(MAGMA) I:=[42, 189, 434]; [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) = 49*n^2-7;

CROSSREFS

Cf. A005843, A158485.

Sequence in context: A232329 A115130 A116871 * A154047 A090198 A299056

Adjacent sequences:  A158481 A158482 A158483 * A158485 A158486 A158487

KEYWORD

nonn,easy

AUTHOR

Vincenzo Librandi, Mar 20 2009

STATUS

approved

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Last modified October 23 14:06 EDT 2018. Contains 316528 sequences. (Running on oeis4.)