cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A016165 Expansion of 1/((1-5*x)*(1-11*x)).

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%I A016165 #19 Nov 10 2024 09:24:46
%S A016165 1,16,201,2336,26321,292656,3234841,35661376,392665761,4321276496,
%T A016165 47543807081,523030706016,5753581906801,63290621677936,
%U A016165 696202941972921,7658262879280256,84241044259973441,926652249799160976
%N A016165 Expansion of 1/((1-5*x)*(1-11*x)).
%H A016165 Harvey P. Dale, <a href="/A016165/b016165.txt">Table of n, a(n) for n = 0..959</a>
%H A016165 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (16,-55).
%F A016165 a(n) = (11^(n+1) - 5^(n+1))/6. - Al Hakanson (hawkuu(AT)gmail.com), Jan 07 2009
%F A016165 a(n) = 11*a(n-1) + 5^n, a(0)=1. - _Vincenzo Librandi_, Feb 09 2011
%F A016165 E.g.f.: (1/6)*(11*exp(11*x) - 5*exp(5*x)). - _G. C. Greubel_, Nov 10 2024
%t A016165 Table[(11^(n+1)-5^(n+1))/6, {n,0,30}] (* _Vladimir Joseph Stephan Orlovsky_, Feb 08 2011 *)
%t A016165 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 A016165 (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 A016165 (SageMath)
%o A016165 A016165=BinaryRecurrenceSequence(16,-55,1,16)
%o A016165 [A016165(n) for n in range(31)] # _G. C. Greubel_, Nov 10 2024
%Y A016165 Cf. A016161.
%K A016165 nonn
%O A016165 0,2
%A A016165 _N. J. A. Sloane_