A048710 Family 1 "Rule 90 x Rule 150 Array" read by antidiagonals.

1, 5, 7, 17, 27, 21, 85, 119, 65, 107, 257, 427, 325, 455, 273, 1285, 1799, 1105, 1755, 1365, 1911, 4369, 6939, 5397, 7607, 4097, 6827, 5189, 21845, 30583, 16705, 27499, 20485, 28679, 17745, 28123, 65537

Offset: 0

Author

Antti Karttunen, Mar 18 1999

Keywords

• nonn
• tabl

Comments

Infinitely many one-dimensional cellular automaton rules (given in sequence A048705) occur in this array, as combinations of CA-rules "90" (generates rows) and "150" (generates columns).

No pattern occurs twice in such arrays.

Each row/column can be generated from its predecessor row/column with SHIFTXORADJ transformation, given in A048711.

Examples

			   1  5  17   85  257 1105 ... [ beginning of array ]
   7 27 119  427 1799 ...
  21 65 325 1105 5397 ...
		

Links

• Index entries for sequences related to cellular automata
• More information

Crossrefs

Rows = A038183, A048711, A048713, columns = A038184, A048712, A048713, diagonal = A048709. Cf. A048720.

Programs

Maple

trinv := n -> floor((1+sqrt(1+8*n))/2); # Gives integral inverses of the triangular numbers

Formula

a(n) = rule150(rule90(1, (((trinv(n)-1)*(((1/2)*trinv(n))+1))-n)), (n-((trinv(n)*(trinv(n)-1))/2))).