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A133179 A modular binomial sum transform of 2^n .

%I A133179 #11 Aug 11 2017 06:07:19
%S A133179 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 A133179 1285,3855,4369,13107,21845,65535,1,3,5,15,17,51,85,255,257,771,1285,
%U A133179 3855,4369,13107,21845,65535
%N A133179 A modular binomial sum transform of 2^n .
%H A133179 G. C. Greubel, <a href="/A133179/b133179.txt">Table of n, a(n) for the first 50 rows, flattened</a>
%F A133179 a(n) = Sum_{k=0..floor(n/2)} mod(binomial(n,k),2) * 2^k.
%e A133179 A034868 is:
%e A133179 1;
%e A133179 1;
%e A133179 1, 2;
%e A133179 1, 3;
%e A133179 1, 4, 6;
%e A133179 1, 5, 10 ;...
%e A133179 A034868 modulo 2:
%e A133179 1;
%e A133179 1;
%e A133179 1, 0;
%e A133179 1, 1;
%e A133179 1, 0, 0;
%e A133179 1, 1, 0 ;...
%e A133179 a(0)=1*2^0 = 1;
%e A133179 a(1)=1*2^0 = 1;
%e A133179 a(2)=1*2^0+0*2^1 = 1;
%e A133179 a(3)=1*2^0+1*2^1 = 3;
%e A133179 a(4)=1*2^0+0*2^1+0*2^2 = 1
%e A133179 a(5)=1*2^0+1*2^1+0*2^2 = 3
%t A133179 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 A133179 Cf. A034868, A048896, A101692, A130047.
%K A133179 nonn,tabf
%O A133179 0,4
%A A133179 _Philippe Deléham_, Oct 10 2007