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A249779 Row "sums" of Pascal triangle (A007318), using operation <+> defined in comment in A245618.

%I A249779 #20 Apr 17 2016 09:15:55
%S A249779 1,2,2,2,2,22,20,28,2,494,912,1672,2376,4836,4160,4184,2,131038,
%T A249779 261800,522272,1035804,2053288,3977272,7742352,13942968,28016020,
%U A249779 47111040,84948528,92072064,272727022,249686810,167376688,2,8589934526,17179867992,34359725136
%N A249779 Row "sums" of Pascal triangle (A007318), using operation <+> defined in comment in A245618.
%C A249779 Operation <+> is defined in A245618 as: k<+>m = |k+(-1)^(k+m)*m|.
%C A249779 a(n)=2 for n=1,2,3,4,8,16,32,64,128,256,...
%H A249779 Michael De Vlieger, <a href="/A249779/b249779.txt">Table of n, a(n) for n = 0..1000</a>
%e A249779 For n=4, we have row 1,4,6,4,1.
%e A249779 By definition of <+>, we find 1<+>4=3, 3<+>6=3, 3<+>4=1, 1<+>1=2. So a(4)=2.
%t A249779 a249779[n_Integer] := Module[{m0082, pls, lst},
%t A249779   m0082[j_] := Table[Binomial[j, k], {k, 0, j}];
%t A249779   pls[k_, m_] := Abs[k + (-1)^(k + m)*m];
%t A249779   lst = m0082[n];
%t A249779   For[i = 0, i < n, i++, lst[[2]] = pls[lst[[1]], lst[[2]]];
%t A249779    lst = Drop[lst, 1]];
%t A249779   lst[[1]]
%t A249779 ]; a249779 /@ Range[35] (* _Michael De Vlieger_, Nov 23 2014 *)
%t A249779 parityAdd[a_,b_]:=Abs[a+b (-1)^(a+b)];
%t A249779 Map[Fold[parityAdd,First[#],Rest[#]]&[Binomial[#,Range[0,#]]]&,Range[0,35]] (* _Peter J. C. Moses_, Dec 01 2014 *)
%Y A249779 Cf. A007318, A245618, A245619, A249388.
%K A249779 nonn
%O A249779 0,2
%A A249779 _Vladimir Shevelev_, Nov 05 2014
%E A249779 More terms from _Peter J. C. Moses_, Nov 05 2014