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1, 23, 89, 199, 353, 551, 793, 1079, 1409, 1783, 2201, 2663, 3169, 3719, 4313, 4951, 5633, 6359, 7129, 7943, 8801, 9703, 10649, 11639, 12673, 13751, 14873, 16039, 17249, 18503, 19801, 21143, 22529, 23959, 25433, 26951, 28513, 30119, 31769
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OFFSET
| 0,2
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COMMENTS
| From the identity (22*n^2+1)^2 -(121*n^2+11)*(2*n)^2 = 1 we derive a(n)^2 - A158536(n) * A005843(n)^2 = 1.
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LINKS
| Vincenzo Librandi, Table of n, a(n) for n = 0..10000
Index to sequences with linear recurrences with constant coefficients, signature (3,-3,1).
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FORMULA
| G.f.: (1+20*x+23*x^2)/(1-x)^3.
a(n) = 3*a(n-1) -3*a(n-2) +a(n-3).
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MATHEMATICA
| LinearRecurrence[{3, -3, 1}, {1, 23, 89}, 50] (* Vincenzo Librandi, Feb 12 2012 *)
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PROG
| (MAGMA) I:=[1, 23, 89]; [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 10 2012
(PARI) for(n=1, 40, print1(22*n^2 + 1", ")); \\ Vincenzo Librandi, Feb 10 2012
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CROSSREFS
| Cf. A005843, A158536.
Sequence in context: A044591 A050255 A014088 * A117049 A142062 A050529
Adjacent sequences: A158534 A158535 A158536 * A158538 A158539 A158540
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KEYWORD
| nonn,easy,changed
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AUTHOR
| Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Mar 21 2009
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EXTENSIONS
| Comment rewritten, a(0) added - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Oct 16 2009
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