A133179 A modular binomial sum transform of 2^n .
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, 1285, 3855, 4369, 13107, 21845, 65535, 1, 3, 5, 15, 17, 51, 85, 255, 257, 771, 1285, 3855, 4369, 13107, 21845, 65535
Offset: 0
Examples
A034868 is: 1; 1; 1, 2; 1, 3; 1, 4, 6; 1, 5, 10 ;... A034868 modulo 2: 1; 1; 1, 0; 1, 1; 1, 0, 0; 1, 1, 0 ;... a(0)=1*2^0 = 1; a(1)=1*2^0 = 1; a(2)=1*2^0+0*2^1 = 1; a(3)=1*2^0+1*2^1 = 3; a(4)=1*2^0+0*2^1+0*2^2 = 1 a(5)=1*2^0+1*2^1+0*2^2 = 3
Links
- G. C. Greubel, Table of n, a(n) for the first 50 rows, flattened
Programs
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Mathematica
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 *)
Formula
a(n) = Sum_{k=0..floor(n/2)} mod(binomial(n,k),2) * 2^k.