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 A077957 Powers of 2 alternating with zeros. 36

%I

%S 1,0,2,0,4,0,8,0,16,0,32,0,64,0,128,0,256,0,512,0,1024,0,2048,0,4096,

%T 0,8192,0,16384,0,32768,0,65536,0,131072,0,262144,0,524288,0,1048576,

%U 0,2097152,0,4194304,0,8388608,0,16777216,0,33554432,0,67108864,0,134217728,0,268435456

%N Powers of 2 alternating with zeros.

%C Normally sequences like this are not included, since with the alternating 0's deleted it is already in the database.

%C Inverse binomial transform of A001333. - _Paul Barry_, Feb 25 2003

%C "Sloping binary representation" of powers of 2 (A000079), slope=-1 (see A037095 and A102370). - _Philippe DELEHAM_, Jan 04 2008

%C 0,1,0,2,0,4,0,8,0,16,...is the inverse binomial transform of A000129 (Pell numbers). - _Philippe DELEHAM_, Oct 28 2008

%C Number of maximal self-avoiding walks from the NW to SW corners of a 3-by-n grid.

%C Row sums of the triangle in A204293. - _Reinhard Zumkeller_, Jan 14 2012

%C Pisano period lengths: 1, 1, 4, 1, 8, 4, 6, 1, 12, 8, 20, 4, 24, 6, 8, 1, 16, 12, 36, 8, ... - _R. J. Mathar_, Aug 10 2012

%H <a href="/index/Rea#recLCC">Index to sequences with linear recurrences with constant coefficients</a>, signature (0,2).

%F G.f.: 1/(1-2x^2). E.g.f.: cosh(x sqrt(2)).

%F a(n) = (1 - n mod 2) * 2^floor(n/2).

%F a(n) = sqrt(2)^n*(1+(-1)^n)/2. - _Paul Barry_, May 13 2003

%o (PARI) a(n)=if(n<0|n%2,0,2^(n/2))

%o a077957 = sum . a204293_row -- _Reinhard Zumkeller_, Jan 14 2012

%Y Cf. A000079, A077966.

%Y Column k=3 of A219946. - _Alois P. Heinz_, Dec 01 2012

%K nonn,easy

%O 0,3

%A _N. J. A. Sloane_, Nov 17 2002

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