A094015 - OEIS

%I #39 Sep 08 2022 08:45:13

%S 1,4,8,32,64,256,512,2048,4096,16384,32768,131072,262144,1048576,

%T 2097152,8388608,16777216,67108864,134217728,536870912,1073741824,

%U 4294967296,8589934592,34359738368,68719476736,274877906944

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

%C Row sums of triangle A135838. - _Gary W. Adamson_, Dec 01 2007

%C Row sums of triangle A152842. - _Reinhard Zumkeller_, May 01 2014

%H Reinhard Zumkeller, <a href="/A094015/b094015.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Di#divseq">Index to divisibility sequences</a>

%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (0,8).

%F a(n) = 2^(3*n/2)*(1 + sqrt(2) + (-1)^n*(1 - sqrt(2)))/2.

%F a(n) = (1/4)*(3 + (-1)^n)*8^floor((n+1)/2). - _Paul Barry_, Jul 14 2004

%F 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 a(n) = 2^A007494(n). - _Paul Barry_, Aug 18 2007

%F a(n) = A016116(n+1)*A000079(n). - _R. J. Mathar_, Jul 08 2009

%F a(n+3) = a(n+2)*a(n+1)/a(n). - _Reinhard Zumkeller_, Mar 04 2011

%F a(n) = 8^floor(n/2)*A010685(n). - _G. C. Greubel_, Nov 22 2021

%p a:=n->mul(3-(-1)^j,j=1..n):seq(a(n),n=0..25); # _Zerinvary Lajos_, Dec 13 2008

%t Table[8^Floor[n/2]*Mod[4^n, 5], {n, 0, 30}] (* _G. C. Greubel_, Nov 22 2021 *)

%o (Haskell)

%o a094015 = sum . a152842_row  -- _Reinhard Zumkeller_, May 01 2014

%o (Magma) [2*8^Floor((n-1)/2)*(3+(-1)^n): n in [0..30]]; // _G. C. Greubel_, Nov 22 2021

%o (Sage) [8^(n//2)*(4^n%5) for n in (0..30)] # _G. C. Greubel_, Nov 22 2021

%Y Cf. A010685, A094014, A135838, A152842.

%K easy,nonn

%O 0,2

%A _Paul Barry_, Apr 21 2004