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

0,2

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,...

Links

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

Example

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.

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 *)

Crossrefs

Cf. A007318, A245618, A245619, A249388.

Sequence in context: A100687 A067096 A259704 * A167394 A029627 A075182

Adjacent sequences: A249776 A249777 A249778 * A249780 A249781 A249782

Keyword

nonn

Author

Vladimir Shevelev, Nov 05 2014

Extensions

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

Status

approved