A163072 - OEIS

%I #6 Sep 08 2022 08:45:46

%S 4,25,170,1200,8600,62000,448000,3240000,23440000,169600000,

%T 1227200000,8880000000,64256000000,464960000000,3364480000000,

%U 24345600000000,176166400000000,1274752000000000,9224192000000000,66746880000000000

%N a(n) = ((4+sqrt(5))*(5+sqrt(5))^n + (4-sqrt(5))*(5-sqrt(5))^n)/2.

%C Binomial transform of A108404 without initial 1. Fifth binomial transform of A163141.

%H G. C. Greubel, <a href="/A163072/b163072.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (10,-20).

%F a(n) = 10*a(n-1) - 20*a(n-2) for n > 1; a(0) = 4, a(1) = 25.

%F G.f.: (4-15*x)/(1-10*x+20*x^2).

%t LinearRecurrence[{10, -20}, {4, 25}, 30] (* _G. C. Greubel_, Jan 08 2018 *)

%o (Magma) Z<x>:=PolynomialRing(Integers()); N<r>:=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

%o (PARI) x='x+O('x^30); Vec((4-15*x)/(1-10*x+20*x^2)) \\ _G. C. Greubel_, Jan 08 2018

%Y Cf. A108404, A163141.

%K nonn

%O 0,1

%A Al Hakanson (hawkuu(AT)gmail.com), Jul 20 2009

%E Edited and extended beyond a(5) by _Klaus Brockhaus_, Jul 21 2009