Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I #18 May 09 2024 04:43:11
%S 1,5,8,20,32,80,128,320,512,1280,2048,5120,8192,20480,32768,81920,
%T 131072,327680,524288,1310720,2097152,5242880,8388608,20971520,
%U 33554432,83886080,134217728,335544320,536870912,1342177280,2147483648
%N a(0)=1, a(1)=5, a(n+2)=4a(n), n>0.
%C Binomial transform is A080926 (without leading zero).
%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (0,4)
%F G.f.: (1+5*x+4*x^2)/((1+2*x)*(1-2*x)).
%F E.g.f.: (9*exp(2*x)-exp(-2*x))/4-exp(0).
%F a(n) = (9*2^n-(-2)^n)/4-0^n.
%t Join[{1},LinearRecurrence[{0,4},{5,8},30]] (* _Harvey P. Dale_, Sep 12 2013 *)
%Y Cf. A080926, A104721.
%K nonn,easy
%O 0,2
%A _Paul Barry_, May 30 2003