A117998 - OEIS (original) (raw)

A117998

Decimal number generated by the binary bits of the n-th generation of the Rule 102 elementary cellular automaton.

4

1, 6, 20, 120, 272, 1632, 5440, 32640, 65792, 394752, 1315840, 7895040, 17895424, 107372544, 357908480, 2147450880, 4295032832, 25770196992, 85900656640, 515403939840, 1168248930304, 7009493581824, 23364978606080

LINKS

Eric Weisstein's World of Mathematics, Rule 102

FORMULA

Bala's observation is correct, and follows from the formula given below and from the fact that this is the central diagonal of square array A099884.

a(n) = A000079(n) * A001317(n). [See Eric Weisstein's World of Mathematics -link]

a(0) = 1; for n > 0, a(n) = A048726(a(n-1)).

(End)

EXAMPLE

1; 1, 1, 0; 1, 0, 1, 0, 0; 1, 1, 1, 1, 0, 0, 0; 1, 0, 0, 0, 1, 0, 0, 0, 0; ...

MATHEMATICA

NestList[BitXor[4#, 2#]&, 1, 50] (* Paolo Xausa, Oct 04 2023 *)

PROG

(Python)

def A117998(n): return sum((bool(~n&n-k)^1)<<k for k in range(n+1))<<n # Chai Wah Wu, May 03 2023

CROSSREFS

Iterates of A048726, starting from a(0) = 1.