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Search: id:A161727
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| A161727 |
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a(n) = ((2+sqrt(3))*(4+sqrt(3))^n-(2-sqrt(3))*(4-sqrt(3))^n)/sqrt(12). |
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+0
1
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| 1, 6, 35, 202, 1161, 6662, 38203, 219018, 1255505, 7196806, 41252883, 236464586, 1355429209, 7769394054, 44534572715, 255274459018, 1463246226849, 8387401847558, 48077013831427, 275579886633162, 1579637913256745
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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Fourth binomial transform of A133626, binomial transform of A140766.
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FORMULA
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a(n) = 8*a(n-1)-13(n-2) for n > 1; a(0) = 1, a(1) = 6.
G.f.: (1-2*x)/(1-8*x+13*x^2). [From Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Jun 19 2009]
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MAPLE
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seq(expand(((2+sqrt(3))*(4+sqrt(3))^n-(2-sqrt(3))*(4-sqrt(3))^n)/sqrt(12)), n = 0 .. 20); [From Emeric Deutsch (deutsch(AT)duke.poly.edu), Jun 20 2009]
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PROGRAM
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(PARI) {default(debug, 0); F=nfinit(x^2-3); for(n=0, 20, print1(nfeltdiv(F, ((2+x)*(4+x)^n-(2-x)*(4-x)^n), (2*x))[1], ", "))} [From Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Jun 19 2009]
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CROSSREFS
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Cf. A133626, A140766.
Sequence in context: A131435 A079027 A081105 this_sequence A121838 A001109 A144638
Adjacent sequences: A161724 A161725 A161726 this_sequence A161728 A161729 A161730
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KEYWORD
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nonn
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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 beyond a(6) by Klaus Brockhaus (klaus-brockhaus(AT)t-online.de) and Emeric Deutsch (deutsch(AT)duke.poly.edu), Jun 19 2009
Edited by Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Jul 05 2009
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