A036214 Bit-reversing masks for 2*n bits.

0, 18, 4740, 17966088, 1136090292240, 1171507928472027168, 19496308761789043518734400, 5212738348288268369644435170918528, 22344471816287582119092726913736555148345600, 1533995044405866391626076022957811770200509055768723968

Offset: 0

Author

Antti Karttunen

Keywords

• nonn
• nice

References

• R. Schroeppel: DECsystem-10/20 Processor Reference Manual AA-H391A-TK, Chapter 2, User Operations, section 2.15: Programming Examples: Reversing Order of Digits.

Links

• M. Beeler, R. W. Gosper, and R. Schroeppel, A Bit-Reversing Example in HAKMEM (Item 167).
• Bitsavers, DECsystem-10 DECSYSTEM-20 Processor Reference Manual AA-H391A-TK, Fifth Edition, July 1980 (Updated, June 1982). (Section 2.15, Programming Examples, example "Reversing Order of Digits" on p. 2-116, page 177 of PDF)
• Antti Karttunen, A Simple C program Demonstrating Bit Reversals.
• Index entries for sequences related to binary expansion of n.

Crossrefs

Cf. A036213, A036215.

Programs

Mathematica

Table[2^n*(2^(2*n^2 + 3*n + 1) + 2^(2*n^2 + 2*n) - 2^(3*n + 1) - 1)/(2^(2*n + 1) - 1), {n, 0, 10}] (* Wesley Ivan Hurt, Jun 10 2024 *)

PARI

A036214(n) = 2^n * ( 2^(2*n^2+3*n+1) + 2^(2*n^2+2*n) - 2^(3*n+1) - 1 ) / (2^(2*n+1) - 1); \\ Antti Karttunen, Jan 14 2024

Formula

a(n) = 2^n * ( 2^(2*n^2+3*n+1) + 2^(2*n^2+2*n) - 2^(3*n+1) - 1 ) / (2^(2*n+1) - 1).

log(a(n)) ~ log(4) * n ^ 2. - Bill McEachen, Jul 13 2024