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A133179 A modular binomial sum transform of 2^n . 3

%I

%S 1,1,1,3,1,3,5,15,1,3,5,15,17,51,85,255,1,3,5,15,17,51,85,255,257,771,

%T 1285,3855,4369,13107,21845,65535,1,3,5,15,17,51,85,255,257,771,1285,

%U 3855,4369,13107,21845,65535

%N A modular binomial sum transform of 2^n .

%H G. C. Greubel, <a href="/A133179/b133179.txt">Table of n, a(n) for the first 50 rows, flattened</a>

%F a(n) = Sum_{k=0..floor(n/2)} mod(binomial(n,k),2) * 2^k.

%e A034868 is:

%e 1;

%e 1;

%e 1, 2;

%e 1, 3;

%e 1, 4, 6;

%e 1, 5, 10 ;...

%e A034868 modulo 2:

%e 1;

%e 1;

%e 1, 0;

%e 1, 1;

%e 1, 0, 0;

%e 1, 1, 0 ;...

%e a(0)=1*2^0 = 1;

%e a(1)=1*2^0 = 1;

%e a(2)=1*2^0+0*2^1 = 1;

%e a(3)=1*2^0+1*2^1 = 3;

%e a(4)=1*2^0+0*2^1+0*2^2 = 1

%e a(5)=1*2^0+1*2^1+0*2^2 = 3

%t A133179[n_] := Sum[2^k*Mod[Binomial[n, k], 2], {k, 0, Floor[n/2]}]; Table[A133179[n], {n,0,50}] (* _G. C. Greubel_, Aug 11 2017 *)

%Y Cf. A034868, A048896, A101692, A130047.

%K nonn,tabf

%O 0,4

%A _Philippe Deléham_, Oct 10 2007

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Last modified July 12 05:35 EDT 2020. Contains 335658 sequences. (Running on oeis4.)