OFFSET
1,5
COMMENTS
LINKS
Michael De Vlieger, Table of n, a(n) for n = 1..1275 (rows 1 <= n <= 24, flattened)
A. Barbé, Symmetric patterns in the cellular automaton that generates Pascal's triangle modulo 2, Discr. Appl. Math. 105(2000), 1-38.
Michael De Vlieger, Diagram montage showing 486 XOR-triangles T(n,k)>0 for 3 <= n <= 20.
Michael De Vlieger, Large 50X25 Diagram montage showing 1250 XOR-triangles T(n,k)>0 for 3 <= n <= 24.
Rémy Sigrist, Triangles illustrating the initial terms
Rémy Sigrist, PARI program for A335061
EXAMPLE
The first rows are:
0, 1
0
0, 2
0, 6, 11, 13
0, 14
0, 30, 39, 57
0, 8, 54, 62, 83, 91, 101, 109
The XOR-triangles corresponding to the 8 terms of row 7 are (with dots instead of 0's for clarity):
T(7,1) = 0: T(7,2) = 8: T(7,3) = 54: T(7,4) = 62,
. . . . . . . . . . 1 . . . . 1 1 . 1 1 . . 1 1 1 1 1 .
. . . . . . . . 1 1 . . 1 . 1 1 . 1 1 . . . . 1
. . . . . . 1 . 1 . 1 1 . 1 1 1 . . . 1
. . . . 1 1 1 1 . 1 1 . 1 . . 1
. . . . . . 1 . 1 1 . 1
. . . . 1 1 1 1
. . . .
T(7,5) = 83: T(7,6) = 91: T(7,7) = 101: T(7,8) = 109:
1 . 1 . . 1 1 1 . 1 1 . 1 1 1 1 . . 1 . 1 1 1 . 1 1 . 1
1 1 1 . 1 . 1 1 . 1 1 . . 1 . 1 1 1 . 1 1 . 1 1
. . 1 1 1 . 1 1 . 1 1 1 1 . . 1 . 1 1 .
. 1 . . 1 . 1 1 . . 1 . 1 1 . 1
1 1 . 1 1 . . 1 1 . 1 1
. 1 . 1 1 . 1 .
1 1 1 1
MATHEMATICA
Table[Select[Range[0, 2^n - 1], Block[{k = #, w}, (Reverse /@ Transpose[#] /. -1 -> Nothing) == w &@ MapIndexed[PadRight[#, n, -1] &, Set[w, NestList[Map[BitXor @@ # &, Partition[#, 2, 1]] &, PadLeft[IntegerDigits[k, 2], n], n - 1]]]] &], {n, 12}] // Flatten (* Michael De Vlieger, May 24 2020 *)
PROG
(PARI) See Links section.
CROSSREFS
KEYWORD
nonn,base,tabf
AUTHOR
Rémy Sigrist, May 21 2020
STATUS
approved