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A164038
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Expansion of (5-19*x)/(1-10*x+23*x^2).
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3
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5, 31, 195, 1237, 7885, 50399, 322635, 2067173, 13251125, 84966271, 544886835, 3494644117, 22414043965, 143763624959, 922113238395, 5914569009893, 37937085615845, 243335768930911, 1560804720144675, 10011324516035797
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,1
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COMMENTS
| Binomial transform of A161731 without initial 1. Fifth binomial transform of A164095. Inverse binomial transform of A164110.
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LINKS
| Vincenzo Librandi, Table of n, a(n) for n = 0..100
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FORMULA
| a(n) = 10*a(n-1)-23*a(n-2) for n > 1; a(0) = 5, a(1) = 31.
G.f.: (5-19*x)/(1-10*x+23*x^2).
a(n) = ((5+3*sqrt(2))*(5+sqrt(2))^n+(5-3*sqrt(2))*(5-sqrt(2))^n)/2.
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PROG
| (MAGMA) Z<x>:= PolynomialRing(Integers()); N<r>:=NumberField(x^2-2); S:=[ ((5+3*r)*(5+r)^n+(5-3*r)*(5-r)^n)/2: n in [0..19] ]; [ Integers()!S[j]: j in [1..#S] ]; [From Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Aug 10 2009]
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CROSSREFS
| Cf. A161731, A164095, A164110.
Sequence in context: A015540 A014987 A108079 * A084235 A002469 A092636
Adjacent sequences: A164035 A164036 A164037 * A164039 A164040 A164041
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KEYWORD
| nonn
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AUTHOR
| Al Hakanson (hawkuu(AT)gmail.com), Aug 08 2009
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EXTENSIONS
| Edited and extended beyond a(5) by Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Aug 10 2009
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