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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.

A081182 5th binomial transform of (0,1,0,2,0,4,0,8,0,16,...).

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%I A081182 #35 Aug 23 2024 20:09:28
%S A081182 0,1,10,77,540,3629,23870,155233,1003320,6462841,41552050,266875157,
%T A081182 1713054420,10992415589,70523904230,452413483753,2902085040240,
%U A081182 18615340276081,119405446835290,765901642003037,4912691142818700
%N A081182 5th binomial transform of (0,1,0,2,0,4,0,8,0,16,...).
%H A081182 Vincenzo Librandi, <a href="/A081182/b081182.txt">Table of n, a(n) for n = 0..300</a>
%H A081182 S. Falcon, <a href="http://dx.doi.org/10.9734/BJMCS/2014/11783">Iterated Binomial Transforms of the k-Fibonacci Sequence</a>, British Journal of Mathematics & Computer Science, 4 (22): 2014.
%H A081182 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (10,-23).
%F A081182 a(n) = 10a(n-1) - 23a(n-2), a(0)=0, a(1)=1.
%F A081182 G.f.: x/(1 - 10x + 23x^2).
%F A081182 a(n) = ((5 + sqrt(2))^n - (5 - sqrt(2))^n)/(2*sqrt(2)).
%F A081182 a(n) = Sum_{k=0..n} C(n,2k+1) 2^k*5^(n-2k-1).
%F A081182 E.g.f.: exp(5*x)*sinh(sqrt(2)*x)/sqrt(2). - _Ilya Gutkovskiy_, Aug 12 2017
%t A081182 Join[{a=0,b=1},Table[c=10*b-23*a;a=b;b=c,{n,60}]] (* _Vladimir Joseph Stephan Orlovsky_, Jan 27 2011 *)
%t A081182 CoefficientList[Series[x / (1 - 10 x + 23 x^2), {x, 0, 30}], x] (* _Vincenzo Librandi_, Aug 06 2013 *)
%t A081182 LinearRecurrence[{10,-23},{0,1},30] (* _Harvey P. Dale_, Jun 06 2021 *)
%o A081182 (Sage) [lucas_number1(n,10,23) for n in range(0, 21)] # _Zerinvary Lajos_, Apr 26 2009
%o A081182 (Magma) I:=[0, 1]; [n le 2 select I[n] else 10*Self(n-1)-23*Self(n-2): n in [1..30]]; // _Vincenzo Librandi_, Aug 06 2013
%Y A081182 Binomial transform of A081181.
%Y A081182 Cf. A081183.
%K A081182 easy,nonn
%O A081182 0,3
%A A081182 _Paul Barry_, Mar 12 2003