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1, 3, 21, 119, 697, 4059, 23661, 137903, 803761, 4684659, 27304197, 159140519, 927538921, 5406093003, 31509019101, 183648021599, 1070379110497, 6238626641379, 36361380737781, 211929657785303, 1235216565974041
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| a(n)=A001333(n)*A001333(n+1).
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LINKS
| Vincenzo Librandi, Table of n, a(n) for n = 0..1000
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FORMULA
| a(n)=((sqrt(2)+1)^(2n+1)-(sqrt(2)-1)^(2n+1)+2(-1)^n)/4.
a(n)=5a(n-1)+5a(n-2)-a(n-3). - Paul Curtz (bpcrtz(AT)free.fr), May 17 2008
G.f.: (1-x)^2/((1+x)(1-6x+x^2)). [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Sep 17 2008]
a(n)=A078057(n)*A001333(n). [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jul 08 2009]
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MATHEMATICA
| Join[{1}, Table[Numerator[FromContinuedFraction[ContinuedFraction[Sqrt[2], n]]], {n, 2, 50}] * Table[Numerator[FromContinuedFraction[ContinuedFraction[Sqrt[2], n]]], {n, 1, 49}]] (*From Vladimir Joseph Stephan Orlovsky, Jan 15 2011*)
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PROG
| (MAGMA) [Floor(((Sqrt(2)+1)^(2*n+1)-(Sqrt(2)-1)^(2*n+1)+2*(-1)^n)/4): n in [0..30]]; // Vincenzo Librandi, Aug 13 2011
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CROSSREFS
| Cf. A084158, A084175, A001654. Essentially the same as A046727.
Sequence in context: A092634 A178537 A046727 * A117512 A068127 A171137
Adjacent sequences: A084156 A084157 A084158 * A084160 A084161 A084162
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KEYWORD
| easy,nonn
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AUTHOR
| Paul Barry (pbarry(AT)wit.ie), May 18 2003
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