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A094015 Expansion of (1+4*x)/(1-8*x^2).

%I A094015 #39 Sep 08 2022 08:45:13
%S A094015 1,4,8,32,64,256,512,2048,4096,16384,32768,131072,262144,1048576,
%T A094015 2097152,8388608,16777216,67108864,134217728,536870912,1073741824,
%U A094015 4294967296,8589934592,34359738368,68719476736,274877906944
%N A094015 Expansion of (1+4*x)/(1-8*x^2).
%C A094015 Row sums of triangle A135838. - _Gary W. Adamson_, Dec 01 2007
%C A094015 Row sums of triangle A152842. - _Reinhard Zumkeller_, May 01 2014
%H A094015 Reinhard Zumkeller, <a href="/A094015/b094015.txt">Table of n, a(n) for n = 0..1000</a>
%H A094015 <a href="/index/Di#divseq">Index to divisibility sequences</a>
%H A094015 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (0,8).
%F A094015 a(n) = 2^(3*n/2)*(1 + sqrt(2) + (-1)^n*(1 - sqrt(2)))/2.
%F A094015 a(n) = (1/4)*(3 + (-1)^n)*8^floor((n+1)/2). - _Paul Barry_, Jul 14 2004
%F A094015 a(n) = (1 + sqrt(2))*(2*sqrt(2))^n/2 + (1 - sqrt(2))*(-2*sqrt(2))^n/2. Third binomial transform is A002315 (NSW numbers). - _Paul Barry_, Jul 17 2004
%F A094015 a(n) = 2^A007494(n). - _Paul Barry_, Aug 18 2007
%F A094015 a(n) = A016116(n+1)*A000079(n). - _R. J. Mathar_, Jul 08 2009
%F A094015 a(n+3) = a(n+2)*a(n+1)/a(n). - _Reinhard Zumkeller_, Mar 04 2011
%F A094015 a(n) = 8^floor(n/2)*A010685(n). - _G. C. Greubel_, Nov 22 2021
%p A094015 a:=n->mul(3-(-1)^j,j=1..n):seq(a(n),n=0..25); # _Zerinvary Lajos_, Dec 13 2008
%t A094015 Table[8^Floor[n/2]*Mod[4^n, 5], {n, 0, 30}] (* _G. C. Greubel_, Nov 22 2021 *)
%o A094015 (Haskell)
%o A094015 a094015 = sum . a152842_row  -- _Reinhard Zumkeller_, May 01 2014
%o A094015 (Magma) [2*8^Floor((n-1)/2)*(3+(-1)^n): n in [0..30]]; // _G. C. Greubel_, Nov 22 2021
%o A094015 (Sage) [8^(n//2)*(4^n%5) for n in (0..30)] # _G. C. Greubel_, Nov 22 2021
%Y A094015 Cf. A010685, A094014, A135838, A152842.
%K A094015 easy,nonn
%O A094015 0,2
%A A094015 _Paul Barry_, Apr 21 2004