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A164544
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a(n) = 2*a(n-1)+7*a(n-2) for n > 1; a(0) = 1, a(1) = 7.
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4
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1, 7, 21, 91, 329, 1295, 4893, 18851, 71953, 275863, 1055397, 4041835, 15471449, 59235743, 226771629, 868193459, 3323788321, 12724930855, 48716379957, 186507275899, 714029211497, 2733609354287, 10465423189053, 40066111858115
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| Binomial transform of A164640. Inverse binomial transform of A164545.
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LINKS
| Vincenzo Librandi, Table of n, a(n) for n = 0..178
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FORMULA
| a(n) = 2*a(n-1)+7*a(n-2) for n > 1; a(0) = 1, a(1) = 7.
a(n) = ((2+3*sqrt(2))*(1+2*sqrt(2))^n+(2-3*sqrt(2))*(1-2*sqrt(2))^n)/4.
G.f.: (1+5*x)/(1-2*x-7*x^2).
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PROG
| (MAGMA) Z<x>:=PolynomialRing(Integers()); N<r>:=NumberField(x^2-2); S:=[ ((2+3*r)*(1+2*r)^n+(2-3*r)*(1-2*r)^n)/4: n in [0..23] ]; [ Integers()!S[j]: j in [1..#S] ]; [From Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Aug 19 2009]
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CROSSREFS
| Cf. A164640, A164545.
Sequence in context: A092785 A114902 A177369 * A100025 A121157 A038184
Adjacent sequences: A164541 A164542 A164543 * A164545 A164546 A164547
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KEYWORD
| nonn,easy
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AUTHOR
| Al Hakanson (hawkuu(AT)gmail.com), Aug 15 2009
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EXTENSIONS
| Edited and extended beyond a(5) by Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Aug 19 2009
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