A016165 - OEIS

%I #19 Nov 10 2024 09:24:46

%S 1,16,201,2336,26321,292656,3234841,35661376,392665761,4321276496,

%T 47543807081,523030706016,5753581906801,63290621677936,

%U 696202941972921,7658262879280256,84241044259973441,926652249799160976

%N Expansion of 1/((1-5*x)*(1-11*x)).

%H Harvey P. Dale, <a href="/A016165/b016165.txt">Table of n, a(n) for n = 0..959</a>

%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (16,-55).

%F a(n) = (11^(n+1) - 5^(n+1))/6. - Al Hakanson (hawkuu(AT)gmail.com), Jan 07 2009

%F a(n) = 11*a(n-1) + 5^n, a(0)=1. - _Vincenzo Librandi_, Feb 09 2011

%F E.g.f.: (1/6)*(11*exp(11*x) - 5*exp(5*x)). - _G. C. Greubel_, Nov 10 2024

%t Table[(11^(n+1)-5^(n+1))/6, {n,0,30}] (* _Vladimir Joseph Stephan Orlovsky_, Feb 08 2011 *)

%t CoefficientList[Series[1/((1-5x)(1-11x)),{x,0,30}],x] (* or *) LinearRecurrence[{16,-55},{1,16},30] (* _Harvey P. Dale_, Nov 24 2021 *)

%o (Magma) [n le 2 select 16^(n-1) else 16*Self(n-1) -55*Self(n-2): n in [1..31]]; // _G. C. Greubel_, Nov 10 2024

%o (SageMath)

%o A016165=BinaryRecurrenceSequence(16,-55,1,16)

%o [A016165(n) for n in range(31)] # _G. C. Greubel_, Nov 10 2024

%Y Cf. A016161.

%K nonn

%O 0,2

%A _N. J. A. Sloane_