A048711 2nd row of Family 1 "90 X 150 array": generations 0 .. n of Rule 90 starting from seed pattern 7.

7, 27, 119, 427, 1799, 6939, 30583, 109227, 458759, 1769499, 7798903, 27984299, 117901063, 454761243, 2004318071, 7158278827, 30064771079, 115964117019, 511101108343, 1833951035819, 7726646167303

Offset: 0

Author

Antti Karttunen

Keywords

• nonn

Comments

Also generated by applying one generation of "Rule 150" to each term of A038183 or by doing a transformation SHIFTXORADJ(A038183)

Links

• N. J. A. Sloane, Transforms: Maple implementation of binary eXclusive OR (XORnos).

Crossrefs

A048713.

Programs

Maple

# Maple procedure for doing Shift XOR adjacent terms transformation:
SHIFTXORADJ := proc(a) local b,i:
if whattype(a) <> list then RETURN([ ]); fi: if nops(a) <= 1 then RETURN([ ]); fi: b := [ ]:
for i from 2 to nops(a) do b := [ op(b), XORnos((a[ i-1 ]*2),a[ i ]) ]: od: RETURN(b); end:

Formula

a(n) = product('((bit_i((n+1), i)*(2^(2^(i+1))))+1)', 'i'=0..floor_log_2(n+2)) + 2*product('((bit_i(n, i)*(2^(2^(i+1))))+1)', 'i'=0..floor_log_2(n+1));