A048710 - OEIS

%I #13 Jan 02 2017 04:04:24

%S 1,5,7,17,27,21,85,119,65,107,257,427,325,455,273,1285,1799,1105,1755,

%T 1365,1911,4369,6939,5397,7607,4097,6827,5189,21845,30583,16705,27499,

%U 20485,28679,17745,28123,65537

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

%C 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).

%C No pattern occurs twice in such arrays.

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

%H <a href="/index/Ce#cell">Index entries for sequences related to cellular automata</a>

%H <a href="http://www.iki.fi/%7Ekartturi/matikka/r90x150a.htm">More information</a>

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

%e    1  5  17   85  257 1105 ... [ beginning of array ]

%e    7 27 119  427 1799 ...

%e   21 65 325 1105 5397 ...

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

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

%K nonn,tabl

%O 0,2

%A _Antti Karttunen_, Mar 18 1999