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

1, 2, 2, 2, 2, 22, 20, 28, 2, 494, 912, 1672, 2376, 4836, 4160, 4184, 2, 131038, 261800, 522272, 1035804, 2053288, 3977272, 7742352, 13942968, 28016020, 47111040, 84948528, 92072064, 272727022, 249686810, 167376688, 2, 8589934526, 17179867992, 34359725136

Offset: 0

Author

Vladimir Shevelev, Nov 05 2014

Keywords

• nonn

Comments

Operation <+> is defined in A245618 as: k<+>m = |k+(-1)^(k+m)*m|.

a(n)=2 for n=1,2,3,4,8,16,32,64,128,256,...

Examples

			For n=4, we have row 1,4,6,4,1.
By definition of <+>, we find 1<+>4=3, 3<+>6=3, 3<+>4=1, 1<+>1=2. So a(4)=2.
		

Links

• Michael De Vlieger, Table of n, a(n) for n = 0..1000

Crossrefs

Cf. A007318, A245618, A245619, A249388.

Programs

Mathematica

a249779[n_Integer] := Module[{m0082, pls, lst},
  m0082[j_] := Table[Binomial[j, k], {k, 0, j}];
  pls[k_, m_] := Abs[k + (-1)^(k + m)*m];
  lst = m0082[n];
  For[i = 0, i < n, i++, lst[[2]] = pls[lst[[1]], lst[[2]]];
   lst = Drop[lst, 1]];
  lst[[1]]
]; a249779 /@ Range[35] (* Michael De Vlieger, Nov 23 2014 *)
parityAdd[a_,b_]:=Abs[a+b (-1)^(a+b)];
Map[Fold[parityAdd,First[#],Rest[#]]&[Binomial[#,Range[0,#]]]&,Range[0,35]] (* Peter J. C. Moses, Dec 01 2014 *)

Extensions

More terms from Peter J. C. Moses, Nov 05 2014