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.

A090041 a(n) = 10*a(n-1) - 20*a(n-2), a(0)=1, a(1)=6.

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%I A090041 #22 Sep 09 2019 01:23:54
%S A090041 1,6,40,280,2000,14400,104000,752000,5440000,39360000,284800000,
%T A090041 2060800000,14912000000,107904000000,780800000000,5649920000000,
%U A090041 40883200000000,295833600000000,2140672000000000,15490048000000000
%N A090041 a(n) = 10*a(n-1) - 20*a(n-2), a(0)=1, a(1)=6.
%H A090041 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (10,-20).
%F A090041 G.f.: (1-4*x)/(1-10*x+20*x^2) = (1-4*x)/((1-(5-sqrt(5))*x)*(1-(5+sqrt(5))*x)).
%F A090041 E.g.f.: exp(5*x)*(cosh(sqrt(5)*x) + sinh(sqrt(5)*x)/sqrt(5));
%F A090041 a(n) = ((1+sqrt(5))*(5+sqrt(5))^n - (1-sqrt(5))*(5-sqrt(5))^n)/(2*sqrt(5)).
%F A090041 Fifth binomial transform of (1, 1, 5, 5, 25, 25, ...). - _Paul Barry_, Nov 22 2003
%F A090041 3rd binomial transform of Fibonacci(3n+1). - _Paul Barry_, Mar 23 2004
%F A090041 a(n) = Sum_{k=0..n} A117317(n,k)*4^k. - _Philippe Deléham_, Jan 28 2012
%Y A090041 Cf. A090139, A117317.
%K A090041 easy,nonn
%O A090041 0,2
%A A090041 _Paul Barry_, Nov 20 2003