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 A163072 a(n) = ((4+sqrt(5))*(5+sqrt(5))^n + (4-sqrt(5))*(5-sqrt(5))^n)/2. 2
 4, 25, 170, 1200, 8600, 62000, 448000, 3240000, 23440000, 169600000, 1227200000, 8880000000, 64256000000, 464960000000, 3364480000000, 24345600000000, 176166400000000, 1274752000000000, 9224192000000000, 66746880000000000 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 COMMENTS Binomial transform of A108404 without initial 1. Fifth binomial transform of A163141. LINKS G. C. Greubel, Table of n, a(n) for n = 0..1000 Index entries for linear recurrences with constant coefficients, signature (10,-20). FORMULA a(n) = 10*a(n-1) - 20*a(n-2) for n > 1; a(0) = 4, a(1) = 25. G.f.: (4-15*x)/(1-10*x+20*x^2). MATHEMATICA LinearRecurrence[{10, -20}, {4, 25}, 30] (* G. C. Greubel, Jan 08 2018 *) PROG (MAGMA) Z:=PolynomialRing(Integers()); N:=NumberField(x^2-5); S:=[ ((4+r)*(5+r)^n+(4-r)*(5-r)^n)/2: n in [0..19] ]; [ Integers()!S[j]: j in [1..#S] ]; // Klaus Brockhaus, Jul 21 2009 (PARI) x='x+O('x^30); Vec((4-15*x)/(1-10*x+20*x^2)) \\ G. C. Greubel, Jan 08 2018 CROSSREFS Cf. A108404, A163141. Sequence in context: A227693 A175255 A081068 * A278689 A140177 A034494 Adjacent sequences:  A163069 A163070 A163071 * A163073 A163074 A163075 KEYWORD nonn AUTHOR Al Hakanson (hawkuu(AT)gmail.com), Jul 20 2009 EXTENSIONS Edited and extended beyond a(5) by Klaus Brockhaus, Jul 21 2009 STATUS approved

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Last modified August 13 04:54 EDT 2020. Contains 336442 sequences. (Running on oeis4.)