[seqfan] parity of binomials and some carryless products, A175669 - A175672

[Richard Mathar]

These 8 sequences appear highly correlated in pairs: 

http://oeis.org/classic/?q=id:A175672|id:A115845
0,1,2,3,4,5,6,7,8,10,12,14,16,17,20,21,24,28,32,33,34,35,40,42,48,49,56,64,65,66,67,68,69,70,71,80,81,84,85,96,97,98,99,112,113,128,129,130,131,132,133,134,135,136,138,140,142,160,161,162,163,168,170,192,193,

0,1,2,3,4,5,6,7,8,10,12,14,16,17,20,21,24,28,32,33,34,35,40,42,48,49,56,64,65,66,67,68,69,70,71,80,81,84,85,96,97,98,99,112,113,128,129,130,131,132,133,134,135,136,138,140,142,160,161,162,163,168,170,192,

http://oeis.org/classic/?q=id:A175671|id:A048715
0,1,2,4,8,9,16,17,18,32,33,34,36,64,65,66,68,72,73,128,129,130,132,136,137,144,145,146,256,257,258,260,264,265,272,273,274,288,289,290,292,512,513,514,516,520,521,528,529,530,544,545,546,548,576,577,578,580,

0,1,2,4,8,9,16,17,18,32,33,34,36,64,65,66,68,72,73,128,129,130,132,136,137,144,145,146,256,257,258,260,264,265,272,273,274,288,289,290,292,512,513,514,516,520,521,528,


http://oeis.org/classic/?q=id:A175670|id:A048716
0,1,2,3,4,6,8,9,12,16,17,18,19,24,25,32,33,34,35,36,38,48,49,50,51,64,65,66,67,68,70,72,73,76,96,97,98,99,100,102,128,129,130,131,132,134,136,137,140,144,145,146,147,152,153,192,193,194,195,196,198,200,201,

0,1,2,3,4,6,8,9,12,16,17,18,19,24,25,32,33,34,35,36,38,48,49,50,51,64,65,66,67,68,70,72,73,76,96,97,98,99,100,102,128,129,130,131,132,134,136,137,140,144,145,146,147,

http://oeis.org/classic/?q=id:A175669|id:A003714
0,1,2,4,5,8,9,10,16,17,18,20,21,32,33,34,36,37,40,41,42,64,65,66,68,69,72,73,74,80,81,82,84,85,128,129,130,132,133,136,137,138,144,145,146,148,149,160,161,162,164,165,168,169,170,256,257,258,260,261,264,265,

0,1,2,4,5,8,9,10,16,17,18,20,21,32,33,34,36,37,40,41,42,64,65,66,68,69,72,73,74,80,81,82,84,85,128,129,130,132,133,136,137,138,144,145,146,148,149,160,161,162,164,165,168,169,170,256,257,258,260,

They all deal with parities of binomials C(k*n,n) on one hand
and the Finnish way of multiplication in GF(2)[x] on the other. It would
be nice to have some explanations on the mutual correlations
and --from the purely administrative point of view-- comments inserted
when they start to differ.

Richard Mathar