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A146962 a(n) = 10*a(n-1)-19*a(n-2); a(0)=1, a(1)=5. 2

%I

%S 1,5,31,215,1561,11525,85591,636935,4743121,35329445,263175151,

%T 1960492055,14604592681,108796577765,810478516711,6037650189575,

%U 44977410078241,335058747180485,2496016680318271,18594050606753495

%N a(n) = 10*a(n-1)-19*a(n-2); a(0)=1, a(1)=5.

%C Binomial transform of A143648. Inverse binomial transform of A145301.

%H Vincenzo Librandi, <a href="/A146962/b146962.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, -19).

%F a(n) = ((5+sqrt(6))^n+(5-sqrt(6))^n)/2.

%F G.f.: (1-5*x)/(1-10x+19*x^2). [_Philippe Deléham_ and _Klaus Brockhaus_, Nov 05 2008]

%F a(n) = (Sum_{k, 0<=k<=n}A098158(n,k)*5^(2*k)*6^(n-k))/5^n. [_Philippe Deléham_, Nov 06 2008]

%t LinearRecurrence[{10,-19},{1,5},30] (* _Harvey P. Dale_, Apr 27 2014 *)

%t CoefficientList[Series[(1 - 5 x)/(1 - 10 x + 19 x^2), {x, 0, 40}], x] (* _Vincenzo Librandi_, Apr 28 2014 *)

%o (MAGMA) Z<x>:= PolynomialRing(Integers()); N<r6>:=NumberField(x^2-6); S:=[ ((5+r6)^n+(5-r6)^n)/2: n in [0..19] ]; [ Integers()!S[j]: j in [1..#S] ]; // _Klaus Brockhaus_, Nov 05 2008

%Y Cf. A143648, A145301, A098158.

%K nonn,easy

%O 0,2

%A Al Hakanson (hawkuu(AT)gmail.com), Nov 03 2008

%E Extended beyond a(7) by _Klaus Brockhaus_, Nov 05 2008

%E Edited by _Klaus Brockhaus_, Jul 15 2009

%E Name from _Philippe Deléham_ and _Klaus Brockhaus_, Nov 05 2008

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Last modified May 23 11:05 EDT 2019. Contains 323513 sequences. (Running on oeis4.)