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A161731
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Expansion of (1-3*x)/(1-8*x+14*x^2).
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6
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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
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OFFSET
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0,2
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COMMENTS
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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
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Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Index to sequences with linear recurrences with constant coefficients, signature (8,-14).
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FORMULA
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a(n) = ((2+sqrt(2))*(4+sqrt(2))^n+(2-sqrt(2))*(4-sqrt(2))^n)/4.
a(n)=8*a(n-1)-14*a(n-2). [From R. J. Mathar, Jun 18 2009]
a(n) = A081180(n+1) -3*A081180(n). - R. J. Mathar, Jul 19 2012
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PROG
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(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
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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
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nonn,easy
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AUTHOR
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Al Hakanson (hawkuu(AT)gmail.com), Jun 17 2009
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EXTENSIONS
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Extended by R. J. Mathar and Klaus Brockhaus, Jun 18 2009
Edited by Klaus Brockhaus, Jul 05 2009
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STATUS
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approved
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