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A161731
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a(n) = ((2+sqrt(2))*(4+sqrt(2))^n+(2-sqrt(2))*(4-sqrt(2))^n)/4.
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4
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1, 5, 26, 138, 740, 3988, 21544, 116520, 630544, 3413072, 18476960, 100032672, 541583936, 2932214080, 15875537536, 85953303168, 465368899840, 2519604954368, 13641675037184, 73858930936320, 399887996969984
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| Fourth binomial transform of A016116.
Inverse binomial transform of A161734. Binomial transform of A086351. [From R. J. Mathar, Jun 18 2009]
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LINKS
| Vincenzo Librandi, Table of n, a(n) for n = 0..1000
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FORMULA
| a(n)=8*a(n-1)-14*a(n-2). G.f.: (1-3*x)/(1-8*x+14*x^2). [From R. J. Mathar, Jun 18 2009]
G.f.: (1-3*x)/(1-8*x+14*x^2). [From Klaus Brockhaus, Jun 19 2009]
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PROG
| (PARI) {default(debug, 0); F=nfinit(x^2-2); for(n=0, 20, print1(nfeltdiv(F, ((2+x)*(4+x)^n+(2-x)*(4-x)^n), 4)[1], ", "))} [From Klaus Brockhaus, Jun 19 2009]
(MAGMA)[Floor(((2+Sqrt(2))*(4+Sqrt(2))^n+(2-Sqrt(2))*(4-Sqrt(2))^n)/4): n in [0..30]]; // Vincenzo Librandi, Aug 18 2011
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CROSSREFS
| Cf. A016116, A086351, A161734.
Sequence in context: A018903 A083331 A076025 * A049607 A035029 A081569
Adjacent sequences: A161728 A161729 A161730 * A161732 A161733 A161734
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KEYWORD
| nonn
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AUTHOR
| Al Hakanson (hawkuu(AT)gmail.com), Jun 17 2009
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EXTENSIONS
| Extended by R. J. Mathar (mathar(AT)strw.leidenuniv.nl) and Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Jun 18 2009
Edited by Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Jul 05 2009
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