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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; internal format)
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OFFSET
| 1,1
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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.
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LINKS
| Vincenzo Librandi, Table of n, a(n) for n = 1..10000
Vincenzo Librandi, X^2-AY^2=1
Index to sequences with linear recurrences with constant coefficients, signature (3,-3,1).
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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.
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MATHEMATICA
| LinearRecurrence[{3, -3, 1}, {42, 189, 434}, 50]
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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;
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CROSSREFS
| Cf. A005843, A158485.
Sequence in context: A134385 A115130 A116871 * A154047 A090198 A008446
Adjacent sequences: A158481 A158482 A158483 * A158485 A158486 A158487
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KEYWORD
| nonn,easy
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AUTHOR
| Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Mar 20 2009
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